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- '^'T" ^ 

THE ^ 

Young Surveyor's Guide 

O B, A 

New INTRODUCTIOI 

TO THE'T: 

Whole An of Surveying Land^f, 

Both by the CHAIN and all: 
Inftruments now in UCe. 

Now fr^ PubliJFdfrom an Origtnd M. S. 
To which is Added, 
All the ufefiil Qeometrical Defnhiom, Axioms, 
PioilemsmA Thearemr, which reUre ro this Arc. As 
alfo theMeihod of Calling up the Dimenfmns of Ar- 
tificers Work. Very ufirful tor all GcDtlcmca and 
Otheri- 
There is alfo added, ty way of APPENDIX, 

a new way ot Surveying large Trafts of Land, ac- 
cording to the Leirned Mr Wbifton's aad Mr D'ltton't 

New Method of Surveying EngiauJ by Exphfnnt. 

The manner ot malting up and preparing 
Tranfpatenc Colours for Beautifying Maps, Charts, 
Piaures, ify-c. 

The Tables of Artificial Numliers, Sines and 

TangeDts,[o every Dcgrn^andMiDUteohheC^jadranc. 
All which U very much Improved and Corrected, 



By EVJrARD LAURENCE,Satveror. 



LCWDON, pTintd far James KnaptOD, at the Cro«» 
in St P,iul's Churcb-Tard. 1 7 16. 



4/^ 

Hes 

,t3r 






73M^ 



J- 



THE 



J PREFACE 



ALT HO' . there is' little need 
of faying any tbin^ jrj, way of 
Preface to the faSoiving Trea- 
ttfe ; yet Cujloni having made 

■ rC almoft as niceffary ai an Entrances to 
an Houfe ; IjbaO fo far comply with 

, Cufiom as to fay^ That the following Di- 
\ regions for Surveyings die. were put into 

■ fry Hands in M. S. to be Enlarged, Cor- 
reSied and Improved^ in fuch a Manner ' 
as to make them of General XI fe and 
Maf^ fraBice^ according to the modern^ 
Befi, and mofl Improved Methods m 
that Excellent and TJfeful Science, 

HoTV far and htnv well that De/ign- 
and Purpofe hath been purfued in the- 
following Fages^ I muft leave to the In- ^ 
genuous Reader to judge, after I have- 
jufi told him that H* wilt meet meet 
A a- ttfith' 



The Preface. 

with feveral very ufeful Definitions, 
Axioms, Problems am Theorems, wbol- 
Ij new, or at leafi newly applfd. Here 
will he found alfo feveral new Problems 
added, relating to the Art of Dividing 
Land., As alfo a Neiv Method of Sur- 
veying large TraSs of Land, hy Sounds as 
well as ^igbt, hyVertue ofdiftant Explofi- 
ons^ fir {I Invented and Publifl^ed by thofe 
two great Genius's and Improvers of Na- 
tural Hhilofoph)i,tbe Learned Mr Whjfton 
and Mr Ditton. 

I jhall only add^ That to make this 
Treatife of as General Vfe a^ may be, 
the Reader will meet with an ufeful 
ColleEiion of all tranfparent Colours pro- 
■ per for the Beautifying Maps, Charts^ 
&CC. . which perhaps may be thought 
entertaining to the Curious. But if I have 
made the whole Eafy, Natural and In- 
JiruHive, I have gained my End^ and the 
SadsfaSion I aim at* 

Edvard Laurence. ] 
CON- 






« 



CONTENTS. 

GEomettical Dfinitions, Pdg. i 

Maxivu. 5 

Probkmu 10 

Tbeoremt. ig 

Drfmtiom of Right Lket appl/d to a Circle. 30 
Plane Ti i^onometrj. a 2 

PraSical F. igonometrj. .f? 

LeveSittgof Ground: jg 

Ke I^e cfiie iW 0/ Namhsrt. 62 

Meafuring. _ ^3 

Meajmirg Jrt'rji.ers Worh 4,8 

Sarveywg ef L<ati ly the Ch^in. aj 

Surveying of Ljtrd by the fhrie Table. 1 p i 
Sill vejh^^ the Theodolite or Semicircle. 1 y3 
DiviiliiTg of Landt. loy 

SeJucivg Statute Meafure to Cvflomary Mea- 
fare. ,^3 

Laying out A^iP Lmds, ig^ 

keduiit^ rf Plots. 1 j, g 

APPENDIX. 

Taliiig the Gtomd-fhtof a Cty or Corpora- 
tioH. ,^l 

A new iigthod of Sutvcyirg a Qmtry or Ivge 
TraSs of Land. 2iQ. 

FrepJti^ Cohwt for Wa^ivg Maps. 7\6 

The 



The Explication of the Signs and 
Charafters ufed in "the Treatife^ 



'EguaUtj, or eqnal. to. 

Majority^ orgrtater than. 

Mhttritji, or lejftr tbiaii 

Morfy or to be aided. 

Left, or to befubfiraSei. . 

Anfjti vffd in Trigonometry, 

Therefore. 

Pfoportjon, 
•Jt^U nfed m tht Tbeoremu 






errata: 

PAG a. l'nieiS,pmi Teriod afteritp. 4.^?,dcIe•- 
B.^ 5./. 34„r. dividing it.^ 6./. aj.forthefe.r. 
rwo.>7. /. a8, r. preeede-p. 8. (.ai, for another, r.'one 
Point. ^ 9. /. 18, r. Oftahedron.p. p./. as,)-. Icofahe- 
dron. p. iz.'.ii, r.aLiDi.p.i4.I.9,for whoft iidc), 
r. each fide whereof, p. 16./. 17, for are, r. is. ^ 19./. 
13, r. Angles. >. so. /. 23, r.falling.p. 21. i- i, r. per.. 
jd Dcf. p. ax./. II, r. i7thDef. p.as-^- =', r. 13th 
Dd. p. 38. /. aj, r. i,thDef. p. 29. 1. IJ. for may, r. 
wii. p. 31. /. 10. inflcad of f or, r. from. p. 3d./. 3, for 
68. (Si. r. 168. tfi.p. 37. /. ij, for 52—30, r. ai°3o' 
p. 39. /. 8,.r^ 407.6. p. 3J.I a, r. Triwglc for Angle, 
p; 39./. It, r. Acucc Angle b. p. 40./. to, for b, r. bd. 
^4I./. II, foiab, r. cb. p. 41. i. 16, forjOiUir 39* 
aa'p. 4ii. 1.17, ford,r.da.p, 45. /. a, for 639 r. 6,3.9. 
p.5't. /. a9, dele and. p, 53. /. ii,fordt', 8a', r. 51°^ 
Ji'. p. 5J. /. as, forfir, 8x', r. fii", ja'. p. S4.J. x5, 
r. 7i:,a5'. p. 57, /. 17, r. Marks, f . tfo. /. ad, r. he- 
wixi the Quancr. p. 6^.1. &4,r. meacioncd.p. 71./. igj 
r. It is. p. 73./. 19, for Br. 8. p. 88. f. s6, for 29, r. 
Sf p. 8 9./. 9. and 11, fortf, r 4. p. 9S9 /. a, put the 
Word UcduftioDa over the two Right-hand CoJumns p». 
99-'. ij.r. i98irftcadof jy.p. I03./. 17. and 18, for- 
Rod, r, Rood./. 104./. 19, for Roots, r Roods p. 108; 
t. afi, tor Circumfercice,r. Circumlerenror. p. 1 ij, /. 
li, r. pJacinj. p. 127.; i4,r. fi£. pi. p. 166. 1. 9, 
•r Arc, r. Arc of a Circle, p. 167. /. is, r. Circuoi^- 
ft!Tentor,.p. 169. /- ii,/or ,Ji r.-^fj. ;. 185, /. 12,,, 
A-cicbcr of the Product it. 






ADVERTISEMENT. 



LOrdftiips Surveyed, and Maps drawn 
of the fame. Timber Meafured 
and Valued , with other Artificers 
Work i and Dialling in all its Parts, 
Performed by Edward Laurence^ 

He is to be heard of when in Lon- 
don at Mr Senexs at the Globe in 
Salisbury-Court. 

K K In Winter, and at fucK 
Times as he is not Surveying, Gen- 
tlemen may have their Sons or 
Daughters Taught Accompts after 
a Natural, E^fy and Concife Me- 
thjid^ with the Ufe of the Globes and 
Maps, and all other ufeful Parts of 
the Mathematicks. 






/ .\- 



XT 



-^ 



THE 

k Young Surveyors 

[guide: 

L Pradrcal Geometry. 

F 'WF' Defign in this part to lay down tfie 

I firft Principles of Geometry ; and to 

f ■ do it metnodically, to b«gin with 

^' ■ Xefinidons, and the Eiplication of 

W J^m- *^^ moR ordinary Ternrs : To wbich 

^ I fliall add . fome Maximsj wherein Natur^ 

[ Reafon does inflnifltM; andjhen proceed 

■^ 10 Geometrical Problems j and fuch Proixp- 

K iitiom as I And convenient for (his Tra^ 

■ fo'that a Man may be able to give a de-. 

inooflrable Account of what he does. 



a The Toung Surveyor's Guide, 
Geometrical Definitions, 

1 A Point is that which is confidered ar 
^avi^gno manner of Dimenfions: And as 
being indivisible in eve*y refpefl, the Ends 
or Eltiemities of Lines are Points., 

2 Fig.i A Line hasLensth, IwrnoBreadtb^ 
not Tbickneff $ of which there ire two forts, 
lis. right or ftreighf, snd curve or crooked j 
as AB i!s a flreight Line, BC a crooked 
Line. 

3. Fig. 2. An Angle is the meeting of two 
Lines in a Point; provided the, two Linn 
fo meeting, do not make one flreight Line: 
As in the tines AB and AC nvcting to- 
gether in the Poijit A, make .an Angle. 
BAC, which is meafur'd by an Arch of a 
Circle E)E,deftribed from the angular Point 
A as a Center , and intercepted between 
the Lines AC, -and AB, which form it an 
J«gh^ is faid to be equal to, gweater arUft 
than another, according as the Arch which 
iiteafijres ir, contains zsmtny, taore, erfeair 
of the equal Paits into which that Qrcam- 
ference is furpfed rofeedirtded. 

Of which right-lined Angles there are 
three forts, Dial" Right Angled, Acute, and 
Obtufe: vf,htn a Line faHeth perpendicularlj 
upon another, it makeih two right Anglee, 
th»t is, neither Ifsnetb to oa» iide or the 
other. 

Ex^mpk. 



The Tefung Sfirvejf<ir*s Guide. $ | 
Example, i 

ffg. 3. Let CAB be a right Line, DA per- 
pendicular to it, that is to faj, neither lean- 
aog towards B or C, but eiaflily upright, 
then are boih the Angles 9t A, vi-^. IjaB 
and DAC right Angles, and contain in 
eadi juft 90 Degrcfs, or the 4th part of a 
Circle ; but it the Line DA had not been ^ 
Perpendicular, biit bad leaned towards B, 
-then bad DaC been an 'Obtufe Angle, 
or greater then a right Angle ; and DAB, 
an Acute Ar^Uj or kfs ihen aRigbt Angle. 

4.AFigure is that which is comprehended 
under one, or more Lims. 

f.Al] Figures containedjunder three Sides,' 
are c^Ied Triangles, which Euclid divides, 
with refpfd either to ib^ir Angles or Sides. 

£. Fig, 4. An Equilateral Triangle .is tbaQ 
which hath ii8 three Sides equal, as the Tri- 
angle ABC. 

'J.fjgi. AnlfofcelesTrianglejis that which 
hath two Sides equal: As if the two Sides 
■ AB and AC be equal , the Triangle ABC 
is Kcofcelefl. 

8. Pig. 6. A Scelenum^is a Triangle having 
all the three Sirfes nnfqual^as GHr 

9. ¥Jg. 7. A Rcflarg^led Triangle, is tljau 
which halb one right Angle, ae DEF. 

10. P^',S. An Ambligone, or obnife Angled 
Triangle, is that which hath one Obtufe An- 
gle, HailGH. 3 2 Pit^ 



.4 . The Toung Surveyor*! Guide, 

'* ^ • f''&- 9' An Oiygone, or Aaite Angled 
Triangle, it that whofe Angles are all 
- Arutp, as ABC. 

1 7, Fig lo. AS^uareconftJls offoar equal 
Sides, ;ind four right Anglei, as AB. 

1 7. A Paranelogram is a Figure that 
ha'li its two oppofite Sides B parallel. 

i4.P/;g.n. AnOblongRedangle,having, ifs 
oppolite Sides e(|ii«l, and its Aogles tight^ a« 
CB, is railed a long Square or Parallelogram. 
1 5. fig. 1 2. A Rhomfcus,is that whofe Sides 
are all t^ual, but not right Angled, as B. 
, 1 6. tig. 1 1. ARhoinboideSjis that whofe op- 
.pofite Sides and Angles ar^ equal among 
thcmfelves ; but not right Angled, as D.. 

1 7. Fig I -c.Paral lei Lines are fiich as being in 
(he fame Plain will never meet, keeping ftill 
(he fame diOance one from the other ; as 
AB and CD 

I &. Fig. I ;. All oiher four (ided Figures are 
railed Trapezia: Other Figures that are 
contained under 5, 6, 7, or more Sdes, I 
cirlt Irregular, I'olygoneB, as F is an Irre-' 
gul^r Figure, and G is a Trapezia. 

Kote^ Such as are made by the Circum- 
ference of a Circle divided into any Nutfi- 
i>er of eq'ial parts , are regular Figures 5 
having alt their Si^es and Angles cgnaJ, 
and are called froni the Number of Angles 
they conrain, as a Pentagutie, Hexagove, Hep<. 
fiigotie, OSagotie^ &c. Which fignifits a Figure 
,Dt 5, 6, 7 or 3 Angles or Sides, whofe 
■ S.d« 



The Toung Survej^or's Guide. 5 ' 

Sides and Angles are all equal one to an- 
oJher; Fer your better underftailding of ' 
which, obferve the Figures lollott'ing. 

19. Pfg- 16.N0W fappoiing the Sides and - 
Angles robe all equal, (A) is a regular P«(-- 
gane^ (B) a H^x^gone^ and G a Heptagons, Sec. 

20. Fig. 1 7. ACircle is a plain Figure, con- 
tained under one Line only, BDCGE, which 
is called the Pert>phery,in the Middle where- 
of there is a point A, which is called the 
Center j from whence all right Lines that 
are drawn to the Circumference are c- 
qual i ai AB, AC, AD. ■ 

21. The Diameter of a Circle isa rjghe 
Lina drawn through the Center, and tpr- 
minated by the Circumference of theCif-- 
clej thereby dividing it into rwo equ:il' 
parts. 

22. F;^. 1 7.The Semi-diameter or Radius is* 
the halt of the whoL' Diameter; as AC or ' 
AB are Semi-diameters. 

2j. A Chord is 3 flreight Line fiibteiidln^T' 
in ,Arch of a Circle, dividing into two 
parts. 

24.^)^.17. ASemicircle is the half of aCir- 
cle, contained under the Diameter and half ' 
Peiiphery, as DBC or EEC. 

25, Fig. 17. A Quadrant is one fourth part 
ol a Circle; and is made by the interfedti-' 
on of two- Diamiiers perpendicularly, as. 
ADC or ABD. 

B. 3 26. Fi^: 



^: 



^ Tbs Toung Surveyor'r Guide* 

26. Fig. 17. A Segment ii aFigure compre- 
hended under psrt of theQfcumference of a^ 
Circle, and the Chord belonging 10 it, as 
ECG, by the Chord Line EC. 

27. J^/i?i7,ASe£torof aCircleisaFignre 
contained under two Right Lines, drawn ' 
irom the Center A, and rhe Circom- 
ference lying between the fame Linea, as 
ABD. 

23. All Circuroferences,ai alfo like Archep, 
Sines, Tangents, Chords and Secants', are 
roportional to their Radiif That Wy if the 
.adius of one Circle be double, treble, &c, 
the Radius of another : TheCircumference as 
alfo likeArche£(i.e. containing the (zmt nom- 
ber of degrees,) aod (heir Sinet, Tangent*, 
Cliords, &c. of the former will be double, 
treble, Cfc. the Circumference like Arches, - 
iheir Sines, Tangents, (fc. 

29. fig. 19. A Diagonal is aflreif^ht Line 
^rawn from one Angle of any Figare, to- 
ihe oppoCte Angle, asCAfi, 

MATIMS* 

1. Thofe Qjiiantities that are equal t» 
third, are equal betwixt themfelves. 

2. If egualQaantitiesbe added to thofe 
that are equal, the Sums will alfo be e^oal. 

3. If equal Qpantkies be taken away from ' 
thofe that are equal, the Remainden will . 
be equal. 

If 



The Toung Surveyor's Gui^e, 7 

' 4. If yoa add equal Qpantides to onequal, 
fae whole win be unequal. 
' 5. If from equal Quantities you take un- 
'qtial, the Remainder will be unequal. 
' ^. QuaQtities that arc double, triple, qux- 
Iruble Cc. to the fame Quantityj are equal 
imong themielves. 

7. Thofe things which mutally agree to 
nch other, are equal. 
: 8. Right Anglts are equal to one another. 

9. Parallel Lines have a common Per- 
pendicular. 

JDVE rtissment: 

Thtte are two forti of Propofitiom, vis. 
problems and Theorenn. A Problem always ' 
{iropofes fomething to be done: But a The- 
orem is a fpeculative PmpoArion, in which 
Rre confidered the AfTedions add Fropei? 
ties of things already done. 

Of Proportim. 
Multiplied Magnitude, is that w^ich ror - 
tains another Maguittide, a certain Number 
of times [weciftfly. 

Ratio or ReafoD, is the Comparifon of 
two Quantities one with another, wheisby 
one is faid to be bigger or lets than an- 
other; in which Comparifon, that whith 
proceeds, is called the Antecedent, and the 
other the OmfequcBt. ' . 

,■ - B 4 Thofe 



S The Toung Surveyor'^ GuiJiu 

Thore QiuDtitiet onljr admit of Reafbn* 

which being maldplied may exceed eac^ 

other. 

10 TheHomologusTerm* in anyProporti* 

on are the two- Antecedents-, or the two 

Confeqiients. 

Reciprocal Figtires, are fuch is are when 

we compare the Sides of one Figore to the 

Sides of the other, and the Antecedentf, 

and the -Confequents of the Reafoni ara ia 

both Figures. 

Of SoUis^va.. SoJidBediet. 

A Solid Angle, is made by the meet- 
M^g together of feveral plain Angles in 
one point, ami of tbe& there mun be 3 
at lead. 

Like redilineal fblid Figures, »'e fueh 
as are contained under an equal Number 
cf like Plains. 

A Pyramid is a folid Figure , contained 
tinder Plains colleded from one Plain 
to another. 

A Sphere is a fblid Figure, bounded with 
a Surface, to which Supenicies all the flreight 
Lines that cm be drawn from the Center 
are equal. 

The Axis of a Sphere is 3 rightLine drawn 
through the Center to both parts of the 
Circumference, about which, if a Ssmi-circle 
be tum'd, it will beget a Sphere, 



The Toung Surveyor's GuiJei 9 

A Cone is a foHd Figure , arifing 
" from a arcuW Bafe of Breight Lines, end- 
ing in aPoiiit called the, Vertei, or top 
thereof; and the Axis of this Ccne, is a 
right Line drawn from the Veitei to the 
Center of the Bafe , and is called a right 
Cone, -if the Alis be perpendicular to. 
the Bafe, if- noF^ a Sca!en« one^ 

A Cylinder is a MiiA Figure, rifing fronr 
a circular B:ife as the Cone dofs ; but the 
right Line end all in ao equal Circle. 

A Cube is a Solid Figure contained un- 
der 6 equal Squares. 

A Tetrahedron, is a (olid Figure com- 
prehended under 4 eqjal and equilateral 
Triangles 5 fo that its Bafe is equal to 
each fide. 

An O^atredron is- a folid Figure contair.- 
ed under 8 equal and Equilateral Triangles.^ 
'-■Ihii. Dodecahedron, is a folid Figure 
contained under 12 equal equiangular and- 
Equilateral Pentagons. 

Tht Icofiedron, is. a folid Figure con- 
rained under 20 equal and equihterat 
Triangles. • 

Befides thefe five regular Bodies, it's 
iinpoflibleio find any others, i. e to form 
any more regular Bodies than ihefe hft, 
wz. three are made tA Trianglfs, one ot 
Squares, and one of Pentagons. 



%% BaSicat 



lo 7he Toun^ Survty9r*s Guidt, 

Tra&icd Geometry, 

I PROBLEM. I. 

J?f. "T* O tftGt a Perpendicular J from 
so. X ih« Point B on the Line KN. 
Open jour CompilTe* to any faiall di- 
iiance { fet one Foot in B, and wiih tlit 
other makft the 2 Maiki D, G. (his done, 
open the Compafles to any auiveotent 
diflancp, then fet one Foot in D, and 
with the other draw the obfcuic Arch 
GG. 

Again, theCompafles flill keesii^the fame 
tliAance, fet one Foot in the Point <^ and 
defcribe the Arch HH, crofling ihe ter- 
mer in the Pouit A« from which draw 
the Line AB, and it will bt perpendi- 
cular to the given Line KN. 

PROBLEM, U. 

Jv^.ZT.To raife a Perpendicular DBtttpon 
the End of (he Line AB. Open your Com- 
■piffft to any ordinary extent, and fetli^ 
nne Foot upon the point B, Itt the other 
fall at plealure, as at the . Point K, and 
. without Bltering the Compa£res, fet oiM 
Foot in the Point K, and witli the olher 
aofs the Line AB, at D, alfo on the othw 



The Tottng Surveyer*! Gwdc. 1 1 
Side defaibe the Arch EE, then, lay your 
Ruler to D, and K, drtw the Line DKF: 
lallly, from the poim B ro the Inteifeaion 
at g, draw the Line BgD, which it pec- 
peodtcalar to the Line A^ 

PROBLEM III. 

F!g.22,'Vo let/all aPeTpendicuIarA£,to tite 
^ivea Line. RQ,/com the givenPointA^u'hich 
18 oat of the Line BC i having fet the loot 
of the Compailes upon A, with any Inter- 
val, defcribe the Arch BC, which will 
cat the Line RQ, at the points Band O 
Then divide the Line BC into two equal 
parts at the point E. I fay the Line AE 
is perpendicular to RQ. 

PROBLEM IV. 

J^. 2^ From apoint C given i to draw a 
Line CD Parallel to the Line AB given. 

.On the Point C ai on a Center, ftr ike anArch 
of s Circle cutting the Line AB given in 
the Point A : Then fet the Foot of the 
CompafTes any where (at a good Jtfimce 

from A) in. the given Line AB, as B, and 
with the fame Interval ftrike the Arch D : 

-Then take in the CompafUs the Length 

.AB, and. putiag one Foot in C, draw id 
Arch cutting the other in. the Poinf D, 
through C and D,' draw the Line CD, 
and it will be parallel to AB. PfiOS. 



r 



t3 The Toung Sitrv£jror*'s Guide* 

PROB^LBM y. 

Ftg. 24. To dividfl the given nght Line 
AB into two ttpal parts, and at Righl 
Angles. Take in your CompafTo any di- 
llance above half the length of the Lin« 
AB, and felting one Foot in the end A, 
with the plher draw the A'ch CDE, then 
with the fame interval on theGenterB.defcribe 
the Arch FGK, intercepting the former in 
F and G, from which Points draw the Lin* 
FGH, aod it ii done. 

PROBLEM VI. 

A fecond way to draw Lines Farallt4 
to each other. 

Fig. 2 ; . Let- BD he a Line given j to make 
a Line Parjilel imioit, fet one Foot of 
ihe CompiflVs at G, and: with the other 
defcribe an Arch as a e, and do the faine 
at: the other end of the Line, and through 
the uimcfl Convciity, and of thofe two A^ 
ehes diaur the Line IL. 

PROBLEM- Vir. 

A third way how to draw Linei Pa- 
sallel to another Line, which alfo paiTis 
IJMOugh a PoMit afiigned; 



. Go.HjIc 



-7he Toung Surveyor's Guide, j^ 
H^. 26. Let BD bathe given Line, E, the 
Point through u^ch the Parallel muft pafti 
Place one foot of your Compares In £, and 
open them till (he other foot juft touch the 
X'ne BC, and defcdbe (he Archd^j with 
the fame extent in zay part of the given 
Line, fet one foot of' your CompaHet, and 
ftrike the Arch D, then tlirengh the poioS 
E and the utmofl Conveiity of the laft Arch 
draw the line CK, which ii parallel to BD 
aiid through the point E. 

PROBLEM yill . 

^:^.27 Todeftribea Tiiangle.ACB^wKofe 
fides, AC, CB, and AB,fhall be equal to the 
three tides, E, D, and F given, provided 
that any two of thepi be greater than the 
third. Take with your Comfiafrei the Line 
F, fo which make AB equal : Then on the 
Center B- with the diflance t) defcribe the 
Arch z X. Again on A with the Line E def' 
rrifae an Arch cotfing the former in C, theii, 
draw AC, and CB, and it is done. 

PROBLEM IX. 

. Kote^ The very fame way yot] mrty 
make a Triangle e^al to anoibcr Triangle . 



14 Tht Toung Surveyor's Guide^ 
PSOBLBM X. 

Fig. 2%. To make anAogleBACequ'Ito the 
AagleEDFat A the end o(the Line ABgtven. 
Defcribe from the Poiota A lad D as Ceo- 
ters two Arches BC, and EF, with the (ame 
inrerval of the Compaflrij then take the 
diflance EF, and fet it fromB to C, then 
draw the Liae AC, I /ay, the Angles BAG, 
and EDF, are equal. 

PROBLEM XI. 

F^. 39.T0 make a Square BCDE, whofe 
^ea Ihou'd be eqnal to die given Lice A : 
Fiifl, make the Lice EC,e()ual to the Line A, 
and on the end thereof at C, ered the Feipeo- 
dicnlarCD alio equal to theLine A,then with 
the fame diftance, fet one foot in B, flrike 
the Asch k i, and on D defcribe the Arch ^, 
cTofling each other in the point M, which 
will confiitute the Square BCDE; 

PROBLEM Xn. 

J^g. 30 To make a ParallelogramABCDor 
long Square, having one fide equal to A and 
the other to B. This ia like theiormer; let 
two Lines be given you, ,AB and BQ and 
let it be Keqmred to make a Parallelogram 
oi tbmn. Fiift lay down youi Idngeli fide 



The Toung Surveyor* s Guide, 15 
AB «qual to A, and at the end ere£t a p«r- 
pendicular Line equal to yout fitorteft Line 
EC, and fo proceed , as you were taught u 
the laft Problem. 

PROBLEM XIII. 

J^. 31. To inalcc a Rhombus ABCD. 

Make an Angle, as ABC, and make the 
fides AB, BC equal, then taking the length- 
of one of them and fetting your Compafft* 
in A, defcnbe the Arch m m j alfo put one 
FootinCandftrike the ArchnifXaniydraw 
the Liqes DC and D ^ and it's finilhed. 

Nae^ A Rhombus is made by 2 equila.- 
teral 01 Ifofceles Triangles. 

PROBLEM XIV. 

i*^. 3 2. To make a Trapeziam. A B C D, 

which Ihall have one Angle at C egiu) to. 
a'giren ApgleE.andthe four fides equal to 
foor given Lmes, vrc th« Lines f g h i. 

Fig. 52. FirJ^ Make the Line AB equal to 
one of the given Lines, as f. 2dly. Upon the 
point B,(by Prob. 10.) make the Jungle ABC 
equal to the Angle E , makirg the fide CS 
equal to the given Line g. jJ/jf, Take another 
of your given liijes, as the lineh, ,andfet- 
tirg one Foot upon C, wiih the other defcribe 
, the rtrch b b. taftly., Take the fpurth line j 
in your Camsa^es, (ctting; one foot in \ 
with 



i6 The Toun£ Surv^or'f Cnide* 
with the other defcribe the Arch o o, and 
draw the lines DA and'DC, which will con- 
fttute a Trapeziana, the fides whereof are 
equal to the four lines given, and it has an 
Angle equal to the Angle gtren,, which was 
to be done. 

PROBLEM XV. 

K^ 33.T0 divide a Circle ABCD,:n(oanjr 
Number of equal [jarts, not exceedirg Ten. 
Pirft^ D'fcribea Circle, and crofs it with 2 
Diameters, AC and BD, pafling through 
the point or Center E, and make A o and A 
Cfc equal to BE, and join OQ 5 To is OQ, the 
third part of the Circle: then join AB toge- 
fh«r, fo will AB be the fourth partj upon L, 
and thediflaTice LB, defcribe the Arch Bm, 
and join Bm, which line is the 5th part; A£ 
or BE is the fixth part, and LO or LQ. are 
thefevsnth pirt, and k A, will be the •ighih 
part. Divide the Arch QAO into 3 equal 
parts at S, and join SQ,, which will be the - 
ninth part, EM is the tenth part. 

So you may jnike the Figures railed"' 
Ptvtagon^ Hexagon, Heyt^on, OUogon, iVwfu-' 
gotf, !tc. 

PROBLE M XVr. 

Fig 34- Any three points A. B, and C, wliich 
ace not is a ftreigbt L^ne, beinggiven j bow 



Tb^Toung Surveyor J. Guide. 17 
tcrfind the Center Oof the Cirrle BAC* 
which fhall pafs thrpueh tbofe three givm 
Poiots. firpj Set'one foot of the Compaflei 
in one of the giren poiots, as in A, and ex- 
tend the other foot to B,another of theppinlSj 
and draw the Arch of a circle GFD.-^ 
Second^, TheCompaifes not altered, fet one 
foof m B, and with the other crofs the foi* 
mer Afch with two finall Archei in. the 
points D and £, and draw the right Line 
DE,— Tbirdfy, Set oneibotof the Com- 
pafles in the ^d point C i they ftill keeping 
the ^me diflance, and with the other foot 
crofs the firfl drawn Arch GFD , in tht 
points F and G, and draw the right Line 
FG, crafnng the former right line DE, in 
the pwnt Gs fo is O the Center fought forj. 
upon which if you defctibe a Circle at the . 
diftance GA, it fhall pafs through all the } 
given points AB, arid C, as was required. 

PROBLEM XVII. 

How to make an Oval feveral ways. 

Ftg 3 5. Make thretCircles whofe Diameters 
-may be in a ftreight Line, as B : Crofs' the' 
line with another Ft^rpendicuUr to it at the 
center of the middleCirclev as cd \ draw the 
lines ce, ch, dg, dfj fet one Foot of the 
CompalTes in D, and extend the other to g, 
defcribe theArch gf, with the fame eztent^fet- 
ting one foot in c, dcfaibe the other part b e, 
(hen 



1 8 The Voting Surveyor't Gwde. 

then frotntheCenter 0,wiihthedtftanceBO, 
defcribe ihe Arch f BE. Again, with the fame 
difiance on the Centtr Q_ Maibt the Arch 
£AH, Bad it is donp. , . * 

THEOREM I. 

K^gtf.lfsny Triangle QRajith two fides, 
QR, anri QS, egwl ib'.two Mttn qr, and 
qs, in any other TffioRln, ^ct if dlfo the < 
Q. included hy tliofe fides = to < q, inclu- 
ded by the other fides i ^ fajr, each parr in 
one Triangle is = to its correfponding pari 
in the othtr,and therefore the whple Triangle 
QRS ii = the Triangle qrs. 

Demon. Foe fn^rafe the. Triangle qrs 
l)e placed upon the A QRS, the fide qr will 
fall exa^Iy on Q.R ( by thefeventh Maxim ) 
Knd the fide qs will fall on its equal QSibc- 
caufi < Q. = < q fo the point S wjll fall 
on s, and R onT,and therefore the'^ whoIeTri- 
angles, q r s and Q)tS do murally agree, and 
confequently each pait in cne is equal to its 
corre^ndiDg one in the other. 

ScboUum to thefrfi Prop. 

By the fame Reafoning we may Djmon- 
firate the following Theorem. > 

If the fides R S, afid rsof the twd 

Triangle 8 (^S, q r s were equal, and the <s 

adJRceni 






iff-' 




7 


^ 


^ 




^ 


-i-i, 


\ 


1 


g 







7Be Toun^ Sarve^or*s Guide, i ^ 

adj-a«nt to thofe fides in the a Q^RS — to 
•he <8 correfponding to them in the Triangle 
qrs", all the reft, and alfo die TiianBlis them- 
ftlres, will he equal. 

For if the fide q r be put upon the fide ' 
QRjthey will agree {by Maxim "j.) but K- 
«auie the < R = < r, and < S = <Si the 
iide Rq will fill! upon fide RQ., and qs upon 
OS, /. the point q will fall upon the pointQ,t 
(j9T if it fail cut of ^ the hints r j, JJ do not 
fall vpm the Likes ^, ^) therefore thtjt 
aie equal (by tbefevaab Maxim) QZ D. 

THEOREM lU 

T&.37. fe «n Ifoceles TriangletheAigle at 
the mfe oppofite to die equal Legs , are 
equal. 

tet tfie Triangle A C B be ruppofed 
two Trianglei, and the Situation pf one cod* 
ven to that of the other, asi c a; B^catife in 
the two Triangles ACS and b cm, ^e fide 
AC is = the fide b c, and the fide CB is = 
the fide ab, and the Angle C is ^ the Angle 
c, therefoH the Angle at the Bafe A = < b 
by the firJl, which was to be Demonfirated 
for the Angle, B and b are tite &me.. 



tflEOj 



20 The Toung Surveyor's Gtride, 

THEOREMlll ^ 

Fig. 38. If two Triangles have «3ch fide in. 
one equal to itg. correQionding £de in the o- 
ther (that is, « = e/f cb=fi, and ab = ei)- 
they will alfo have = Angles opposite to. 
thofe = fides (that a e = f, a=e,mdb=i). 

Let the lioe ab be put upon the line ei. Then- 
the point c will either fall in f, or it will 
not. If it falls in f, the whole Triangles a^ 
gree, and therefore all (he Angles are equal 
By the feventh Maxim. 

Fig-^^.lic falls out of f, draw the line fc : 
Becaufe by Hypothecs the fldestf, and ac 
are equal, the Angle efc muft he equal to the 
Angle ecf; hy the fecond S'ropo&ion theie-^ 
fore Angle! fe will be greater than Angle ecC 
and Angle ifc wil be much greater than An- 
gle icf. 

Again, by fuppofition , becaufe^ f =:. 
be, < ifc, willbe = to < i e f. Tlierefore- 
i fc is both much greater thaOj and equal ta . 
cf, which is impoiUble , and tberetoie c 
cannot fall out of f. ' 

Tff£OR£i!if iV. 

J^^.40.0ne right line CDfalling on another 

AB, makes the Contiguous Angles = to two 

right Angles. Let the line CD bejperpendi- 

culat to AB, theD the Angles ADC and CDB 

wijl 



The Toung Surveyor's GaiJe* a I 
will be right pr.jDiif! But if the line fall 
obliqueljf as tD, raife theperp!ndicu]ar GD, 
rf!%), becaufc the urieijualAngles ADE and 
IsbB occupy the famepl^ce which the two 
right ones ADC andCDBdid, therefore they 
pgree to two right Angles, and confeguenily 
to them (by 7 M.) Q. £D. 

,--■'■ THEOREM V. 

Fig.^i- If two right lines {BC^mi FL) cut 
one the other in any point (A) the oppniite 
Angles at the Vertex (A) will be equal ; that 
18, the Angle LAB is = to CAF. Becanfe 
BA,,flands upon the right line LF, LAB, 
and FAB will he equal to two right {by the 
fourth Tlmrevi.) Aid becaure FA rtafids up- 
on BC, the Angles' FAC, and FAB, willbe 
equal to.two right (hyt'^efame) therefore (he 
Iwn Angles LiB, and FAB Taken together 
wiil he unal to the two Angles CAF, and 
FAB, i»?en together. But the common 
Angle FAB-being taken away, there remains 
the Angle LAB= CAF (by the third JUax.) 
Q,E.D. 

T.HEQREMi.VI. 

Fig 4.2. If arighi line GO cut the two pa- 
rallel rifthr lines (JB cFjfitfi the alternate 
<(RLO, ^L. W BJ:0,C0I.) are equals. 
SewiUfy, The exteroal Angle (GLB) isequaL 



22 ThfiToung Surveyor's GwHe* 
to the ipternal one (2.0FJ as alfo(< G£,S^ 
<LOC.) Tbirdfy, The two internal Angles 
towards the fame parts together ALO COL— 
to two right Angles : Alfo the <s BLO, fOL 
together = to two right Angles. 

DmoH. oF the firft part Draw LQ. and RO 
perpendicalai toCP (rom the points L andO 
and they will be alfo pecpeadicolat to AB(by 
the 1 2tb Mjx'm,) now in the AS ROL, LOQ, 
the fide OL, is common to both; R O =LQ. 
(A> tie m Def.Jind .•.<LOR=<LOQ (hy tba 
frft Prop.) alfo <R0 L « < Q.LOV. < 
BLO =:<COL (bjtbefeemiM^x.) which 
is the. Firft Part. 

Second I'arr. Angle LOQ. =<ROL {hj **» 
Tirji Pjtt,) and < RLO= <GLB (bj the yti 
Prop.) :./< LOQ.=< GLB (bi tbejrjl Mvt.) 
afterthe fame manner may <IX)C be proved 
= to < GLR which is the fecood Part. 

Tbe zl Part. Angle GLB=<RLO 
(^ tbe "jtfi Prop.) <COL was proved = < 
RLG (in tbe 2l Part.) bot< RLG -\- < GLB 
= two right <8 (*; tbe ^h Prop.) /. < COL 
"|- < RLO = two right Aoglef , as aUb < 
BLO-t-<FOLQ,E.D. 

THEOREM VIL 

In any Triangle a be, the three Aisles 
taken trgether, are equal to two ri^t ones. 






The Toung Surveyor*! Guide. 23 

DEMONSTRATION. 

/%4^. Let i be drawn parallel ro theBafe 
ac, theo tbc < a will ;=: < dba (by the stb 
B'op.) and < c, = < ebc (^ tbs SiIkPio^.) 
but < d ba -\-.< abc + <: cbe = to two right 
Angle* (hj tbi 4tbFittf.) .*. < a -}- < c -t- < ^ 
abc = two right Q, E. D. 

CO & RO L A RT.l. 

Hf Dce by Having one of the acote Angles 
in any R'dangled a, you m^y find the c-' 
thcr kv takirg ihe Angle out of 90 Df gr»s, 
and that which remaios will be the Angle 
required ; io thatooe Angle is the Comple< 
Dient of the other to 90 Df greet : If your 
Triangle be obnifeoracitfr, any two'of the 
Angles beirg known, the ^d is known « by 
taking (he Sumoi the two Angles known, 
from 1 80 deg. and the remainder is the other 
Angle. 

CORROLJRT. II. 

J^.jj.lfany fide ofaTriangle be produced, 
the external Angle o will be equal to the 
iwo Internal and oppofiie Angles b and e. 
For the Angles b and e together with d, are 
equal to two ri^ht ones (^ the Preced.) and 
(b alfo are the AqglesO and it,(by tbet^tbJ 
where 



14 ^^ Toung Surve^orU Guide, 
whenfore O miift be egaal to b added to 
«, bccauTc tfigdther wiui d, it makei tura 
right ones, as ihey do. Q. E.D. 

CO R^OLJRT. III. 

J^g. 45. The internal Anglet A, B,C,D,E, 
of any Polygon ABCDE are equaUo twice 
as m3ny right Angles as it tiai £dn, except 
foui.For everyPoljg'ja maybe divided into 
as maiiyTri3ng1es,excepttHro,as ithasiides, 
by lines drawn from any Angle D to all the 
T'cft, except the adjoining ones% and Ej but 
each of tnofe Triangles contain three Angles 
= two right ones {by the ytb) therefore all 
the Arigles of any Polygon are equal to twice 
as many right Angles, eieept four. 

CORROLJRT. IV". 

fjg.46- In any PolygonA B CD E, the iidei 
being produced will make all the external 

Argles a, b, c,d, e, equal to four right onea; 
jpor each internal < Awiih its^eiternal •< a, is 
equal to two right Aigles (by tbe^tb j)cOnre- 
quently all the internal and external Angles 
are equal to twice as many right Angles as 
the Figure has Hdes. But ail its internal 
Angles are equal to twiae as many right 
Angles except 4 as it has fides ("iy ibe Ufi Cor.) 
therefore all the external Angles taken- te- 
gither, are equal to four right ones. 

COR,' 



The Voimg Surveyor's Cuiik, a S 
CORROLARTV. 

. From the third Corroldiy ive may de- 
duce a Method lo examine whether the 
Angles of a Fifld be raken light' or tvi^^viz. 
Malliply the number o\ Sides thereof by 2j 
fubflrad 4 from that product, which remain- 
der mulriply'd by 90, will give the Sum 
of all th^ Angles, which Sam mufl be e- 
quil to the Sam of the Angles taken in ih« 
Field if rightly obferv'd. 

Fig.^S For Eiample: L^ABCDEbea 
Field bou:i(led wi:h ^ iiHes, tha Sum of the 
Angles whereof is 540* which is equal to 
tiie Number of fidts (5) maltiply'd by 2» ■ 
and that Ptoduft leffen'd by 4, multiply'd 
by 90, therefore it is very probable that 
thofe Angles were rightly obferv'd. 

TtiEOREM Vm. 

f7^.47.The oppofiteSides and Angles (^any 
Parallelogram are rqjal^ and it is divided 
into two f'guil paitB by ( a Line diawii 
f[om one < to Its oppofite one which is 
called ) a Diagonal Liae. B.'Ciufe O B is 
ptraPel to DC ( h Def. 14.) the < OBD 
= <BDC (by Prop. 6) alfo bec^ufe DO 
and BC are parallel < CBD = < ODG 
( by the fame ) .-. the whole < OBC =s 
< ODG after the fame m4Rnst < O may bi 



^ 



a6 The Toang ttrw/or'T Gttiiif* 
Iheurn to be rq lal to < C. But /ince we 
hare fbewn that rhefe Triangln Q. and 
K which have one fide X) 6 common, and 
two Angles adjacent td D B in one, rqua] 
*fi the rwo correfpontKng Angles in the o- 
iher, fhfiefore thore Tnangle»and iD th*it 
p4:t(,are iqualby theStholii'infortiePrqp. i. 

SCHOLIUM. ' 

Fig. 48. For rheTrianglft AEF and GFD, 
having the Alrernate Angles EAF and FDG, 
and AEF and FGD, and AFand FD tqciil 
they are equnl, (by the 1/, ) and fince the 
Trapezium BfcFD, with the Triangle AEF, 
that is to fay, ihc Triangle ADB, is half the 
Parallelogram, (by tbi hft) the fame Trape- 
aium BEFD, with the TritDgfe FGD, will 
fce hjlt the fame-, therefore the liM £G di- 
vides it iotQ into two <qjal parts. 

THEOREM IX. 

jF^?.4P.ParanelogMmi having thefimfBafi", 
and Ix'ng between the fatne Puralleli, are 
co'ial. For AB - EC &*«. (by the ith) a 
BAF = a (E C G ^ the'jfi) from hoth 6* 
which take away thecommoa a DEF, and 
there will remain the Trapeaiom AEDB = 
Trapezium DCFO, to each of whieh add 
the a BHC and then the Pajailelogrsm 
aBEC ^ iPitallelogmm JBC6 ptr 2i M-x. I 



^i Ttnmg Survejfor's Gmde. 27 

TBEOhBM X. 

Fig. 50. 'f rianglea en the fame Bafe AB, 
mad being between iW fame Parallels CF and 
AB if 9 always pqnal. 

The Triangle ABC, ii f q«al to the 
Triangle ADB. Draw the line I>fi parallel 
to JVC, and the line Bp parallel to AD, then 
th«r« will be mada tiro Pai^llelograins, A 
CDB i and aDFB, which being between ih« 
fame piTblleit afvd 6n the fatne B»fe^ will 1m 
rq'lal to ons anotber (by t6e hfi-^ tut the 
Triangle ACB is the half of the Parallelo- 
gram A B C C. and the Trimble DBA is the 
half of a PiTBlfclogram ABDF, (Sj tbt 8th J 
Therefore the Triangles rt CB andADB^ 
{ muft be vqral, by tiie-6th Max. 

COkROt ARt. 

Trianiles having ■ the fame or rgial 
Bifes Xd PrfratklogMms. and between ihe 
fame iftarallek, «re jaU half thofe Paralleliv 
gram. 

THE OR EM XL 

, ^ i^.jT.TlvrComplem^nta of a Pirallel<i. 
gnurfve rqaal. Ii( (he PikraDelogram ABDC 
the Ct>nlpkni«ms\^£H and £Gbl jr» 

C 2 DEMOA^- 



,28 T^e Tcmg Surveyor*! Curde. 
DEMO NSTATIO N. 

If HG and FI fa-* drawn through 

■nv, paint E of the Diigonal CB paralW 
to Al. and CD, the Parallelogram ACCB is 
divided info lour Parallel<\grams, two of 
rwhich-are about the Diagona), and the other 
two are their Coinplcirifnts, whitli are I hut 
ihewn tebe(^i;il, o ABC = to A CDS 
and the <is H B E and EFG are = to as 

JBE and ECG (hfi) If frdm the Eqiul 
^1 ABC and CDB voa CohRtjQ the F^ual 
A3 HUE, EFCandIBE,CEG there wiU re- 
main theParall'IogramAHEF — to the. Par 

(jrallelogram EGID (by si Jxiom.) 

THEOREM XU. 

F;>.52.In eve»y rpaangte TriangleA B G, 
the Square of the fide AC, which is oppo/ite 
*o :ihe fight AngV, is tgual to the Squares 
of the other two fides (J B, CB) 

D^roon.D.-awIC,BF,andBE,ParalieltoAF. 
I' then you add the coiiimon < B^C <o (he 
right Angles lAB, FAG, and therefore e- 
-qial, llie wholes I AC. !FAB, will be rqial, 
but the <s I AC, FAB have the two fides 
w*i><"h rontaim tho^Angles e<jiiat (iji>/ J ?) 
to wit lA = BA and CA .== FA .-. < lAC 
■^ A FA.R (by Prop, i) hu( A TAG = 4- 
th.t;ga:e ILEA and A ABF=-t ParaUelq- 
^aia 



The Toung Siirveiilrr^s (TuiJe; 39; 
gram AFZ the (b/ Piop.io) tturefore pquare 
LIBA =the PatallelognmAFZE. Ir inighl 
te Ihewn with the fame Eafe that th? Square 
BXCH =lhe Putdlelogltim CZER. Q, t. D. 

T HBO HEM Xllli 

fig.^^.An<{SCA) at the Cetiter 11 double 
to the < (JFB) at the G'truinFerence when 
the fame Arc (AB) is B ife to both Anfiles* 
Thii Prop, hath three Cifia, The fitft in 
when the fide (CJ) coiticides with the fids' 
(.AF). For then CF = CBi becaule both 3t» 
drawa from the Center to the CirctiinFerenr^ 
c£ the Tattle Circle therefore in aCFB-lCBf 
= <CFB (per fnp. j; fciit <BC*=< 
CBF + < CFB (pcrSM. 7 fref.J .-. <; 
ACB is douUe the <CPB which may the (irft 
Li the fecood Cife CA and CB tall with- 
out AF attd BF. Then < X C A i« 
dotible < A FX, atid < XCBiidoobij th» 
<XFB (ijtbefJI-CiJi} Tlierelore the wltiiU 
< ACB is donble the whole < AEB. In ihe 
third Cafe RK cuts C A, and the < AKB :'s 
wholly without the < ACB Draw K C L 
Ihtn < ACL is double < AKL (by tbe frl 
Ctfi) and if < LCB and its double < LK B- 
be taken away there reintins < A B doab.e 
■6 A KB. Q.E.D. 



C 3 THEO-- 



9 o The Toung Survejor't Gurje* 
THEOREM. XIY. 

All fimiW Triasf^lei have their fid^s a- 
bout their fqual Argles nroportiora). For 
if they were inlcribtd in Ciccks, (heir Sides 
would be C hofdi of fimilar Atct. 

THEOREM. XV. 

F^. T4. If in any Triangle a tine be 
drawn parallel to the. Bafe, that Line 
will cut ihe Leg« proportiona!?. In the 
Triangle ABC let the Line DE, be pj- 
rallel to BC : I fey that i^D, is to AD 3s 
AB to A^ and AB : BC :: AD: DE. Alfo 
DE: BC:AD:AB:or AD: AB :; AE: AC. 
For As Atif, and -DHare fitniUr becaHft 

<D=-<!Band-«E= <Q (bj the6th) 
^i(t < A is common to b«h .'. theif 6ides 

about their tqjat Angla are ptoportional 

Of Rijiif Litttt gf plied to a Circle. 

DEFINITIONS, 

I. Every C-rcle is fuppofed to be divid- 
ed into 5^0 D g. and each Dig- iott) ^0 
parts, called Minutes, and each Minute into' 
Poparts, called Seconds, ifc. -^ny Potti-' 
on of the Circumference whereof is an Arch, 
and 



The Ttmng Sitrveyor'i Oiade. 3 1 
and is Meafured by the. Number of Degteet 
it contains. 

2. >■'/.??. A Chord is a Rigl^t Line 
joining the Extremiiiei of an Arch, as 
AC, is the chord of the Arches ABC, AD::. 

3 A Tangent of an Arch w a Ri^th'T 
line drawn Perpendicular to the end of the 
Radius or Semi Dameter, pafllng through 
one end of the Arch, and i(s length is li-, 
mited by a Higiit-line drawn for the Cen- 
ter through ihe.oiher.End of the Arch, which 
is called the Secant i thus BM is the Tan- 
gent, and FM the Secaot of the Arches 
Afiaod AD. 

'4. A Right Siae ia « Righr-lint 
draw* from one End of an Arch, Perpen-- 
dicalar to that Diaimter pa0ing thtoogh' 
the other End , w is half the ( h^rd of tn« 
double Arch; AE it the Right Sine of th» 
Arches AB, and AD- And here 'tis evic'eor, ■ 
that the Sine of 90 D.'g. which is fquilta " 
the Radius, or Semi-diimeter of that i, ircV, - 
is thegreatefl of all Sines, the Sine of au 
Arch greater then a Quadrant, being lefa- 
than the Radius. 

5. A Verfed Sine is the Segment of 
the Diameter intercepted between the 
Arch, and the Right Siw, EBlis the Verfed 
Stne of the Arch AB, and (D of the Arih 
AD. 

6. The difftrerc*! of an Arch from 
' 9. Qaadrant,, whether it' be greater or left, 

C 4., is 



5 2 The Toung Surveyor's Guide: 
is -call'd ifs Compleimnt, GA is the Conv 
t)lemer.t of the Archfs AB, ADj HA is the 
Sine o\ the Complement, or Gjfine, GI the. 
Tangent of that Complement or O-Tao- 
gent, F 1 the S.cant of that Complement, 
or Cc-recant. 

Tlane Trigonometry^ 

Is tbe.Menfiiration of tTi« S (i<s and Ar- 
gles of plain Triangles. A pUin Triangla 
has Jil paits, viz. -Three Sides and three 
Angles, whereof any three being given, ex- 
cept the three. Angles, the other may be ^ 
found by Trigonometiical Calculation. 

In ri^ht Angled Triangles , there are 
feven Cafes, all performed by the follow- 
jng Jxionu. 

J XIO M I. 

In any Right Angle Triangle, if either 
of the Legs be fuppofed to be the Ridius 
' of a Gird!-, the oiher L-g will be the Tan- 
gent of the oppofite An^e or of the Aigle 
at the Center, and (he Hypoibenufe will be 
the Secant of that Angle : But if yon iin 
agine the HypothenuH; to be the Radius of 
a Circle, then each Leg will be the Sine of 
its oppofire Angle, or of the Angle at the 
Center, as is' plain fiom. Fi^. 5^.57: 5S;y9. 
Iq 



The Toung Surveyor's Guide. 33 ^ 

In the firft of which : B: {the Bjfe) being 
made (he Radios, P (the Pirpcndiculur) is 
ihe Tangent of thrAogle nt a,'the Cenrw of 
(he Cirde, which is oppnfite toP, and the 
H/pothenufe is the S cant of the fame Angle. 

In the fccond of which, where P is-oiiide 
the Radius, R js the Targent of the oppo- 
fite Angle at the Center : O. 

In the third of which wher« H theHy- 
pothenufe is made rhe Radius, . P is ihfr 
Right Sine of the oppofite An^le it the 
Center. C 

In the fourth of which H being a^o triads 
Rarfioi, but c the Center of (he Circle, B 
will be Sine of its oppofite. Angle. 

CASE. I. 

J^ 60. HyportienuPe and Aogles giv<n,- 
either ot the Legs required. 



^ be =14457 
la i-a b c, given< S t(qba,and 

Praportitm. 

Ci > <:ba 

<cs!l CC3^ 

\s7 V 168 i 61 - 

S'90':446;:< >22'.3o' -? 



_ 407- 
C 5 O^it*-^ 



/ } 7be Toung Swvejor*s Gmdt, 

Operatun. 

To _ the Lcgar of h c 446, 2. ^44044 

ftdd the Sioe ct Aoglc c 22*.. 30' 9. (82S40 

12. 226884. 
Sum abate, Rad= Log. t>a 168^61. 

By GttBtert Scale. 
The extent from the Sloe 90' , to 
the Sine of the AcgU c 32- 30 od the 
Line of the Sine*, will rfach from b c 44^. 
•o ba 168. &i on the Line of Kjoiberi. 

CASE 11. 

Que Lfg and an Argle glrcni the 
other L'gitquired, 

Exampk. 

In the & al;c,giv<»^ >rr^'d ca, 

^^(Lc,= 22,JO> 
PfoportioM. 
Rad: ba : : c f, ic: ca, le. T, 45,; 168, 
61 :: T, 67,30 '407,^. 
To the Ixgir. ba 168, 6j 2» 2368S4 

add thee t, c 22^30 10, 382776 

Suoi abate,Rad=Lrg, ca407,6 12.6056*0. 

CASE ill 

One Leg and an. Angle givejt, Hyi»lhe-. 
nufe required. 



ExampU. 
In tliej^ab c, given ^ . % if q'lii'd he 

(Tic— 22',30'> 

. S,ic:ba::ttad, : b f . 

Operation. 
Tfl /r,co. S, <c 22°., 30*. o, 4171^0 
Add Lrg^ir, 6a ij58, 61 2, 226S8t 

S^m = Il^e!.:f><: 44^ 2< '^44044 

. - ^ Qvnters Scak. ■ 

-The E«en», from S, i c 22' 30'. To the 
S, 96' y on the Liils of Siges. will reach 
fronibaid^, £1. to be 446 on the Line 
ef Nfimbws. 

c^.yfi rv: 

One I/^ «ad ^ Hypothenufe given, - 
the Angles ftquktd; 

Iatbe^«bC>446^ >req«iredi5 . 

^JfiSj^J Cb 

' FrepanioK. 
Alfcc:Rad,:: ba:S,ic 
446:8,90'': i.i<8. 6i:S22', -30' 






s[6 Tee Towtg Surveyor j fjuide* - 

Operation. 
To Ar,co,Lrgar,bc44* 7. 3?595<S 
, Add Logar, bv. 68, 61. 2. 22688^. 

SumS. Ac 22*, 30' ■ p. 582840 

From. 90°, 00 

Subftrad 22 30. . 



/ 



• Remainder. 6 y'ao* = < 1%, 

By Gmtert Scale, 
The Exrrnt from 446, to i6r, 61 00 the 
.Xineof Kumberi, reaches from S. 90*, 
o the Sine 22', jconthe Liae ot SHnef . 



CASE V. 



One Lrg and the HypothenQfe 'givcD, 
4he other n quired 



'dca 



- Sjbc==446 ? 
sbc.givcBC Wtqoirt 

^b^=i68,6i^- 
ProportioB, 
■^Vbe Angles being lound by the foarth 

As Rad, : c t, < c : { ba : ca; 

T,45:T 67s 30' ; : i6%\ 61 " : 407. 6. 
Ofertttim. 
Tothectj <C22*', 30' lo, 3&277fi 
add the Log. ba i£8, 6r. i. 226084. 

Sim,lefsRad,=:Log,ca407,6 12. ^09660. 



7be Toung Surveyor's Guide, 37 
By Gunteit Ssatr. 
The extent from T, 45', 00' Ion iheLme of 
. To the T,67',30' JTarg-nts 

Reachetfrom 1^8 -61 > on the Line of 
To 407- -6 J Numbew. 

C JSE \I. 

The L^s given, and the Angles re- 
quired. 

Prifportfou. 

c a : b a : : Radius -. Tang, L c, 

407.5: 168. 61 ;:T,4;° : T, 22°^o» 

Operatic!, 

To the Ar, co L?gar. ca 407, 6 7. 390341 

add the L'lgar, ba, i68» 61 2. 226884 

Sum = T, <c, 22—30' $.61722;. 

- By Gimttrs Scale. 

The.Eltem from 407, 6. to 18A. 6i on 
the Line of Numbers , reaches from T, 4;' 
00' to the T, ■ 22°. ^c'on the Line of 
Tangents. 

CASE VII. 
The L'g8 given , the Hypotbehufa r«- 






38 The Timg Sttntfor's Guijt, 

{ac, 40^. 5-1 
S req. b c- 

The Angles being found by the 6th Cafe. 
S. ib:Rad, ;:ac:bc. 
S, 67'. 30' : S. 90' : : 407, 6 ; 44^, 

To ihe Ar.co, S t b 67" . 30' o. 034385 
Bdd -Logar. ac, 407. 6 2. ^09659 

Sum = Logar. b c 446. 2 . 54404^. 

By . Qmtm ScaU. 

The Eitent from S, 67° 3c' j^ «n ihe Line of 

To tfie Sine 90,00 f ^Simi. 

Reaches- ffoin 487: 6 7. on the Line 

• To 44$. o 5 of Nuiribere. 

Of Oblique-Angled Platte Triangles. 

Wherein there ^re 6 Cafei , and all re- 
folded by the three followiitg Axioms. 

J TIO M il 

In all Plane Xnangles, the fidei are pio- 
porrional to the Stfles of their oppofite 
Angla., 

AJTIOM. 






The Toutig Survrfor't QuUe, ' 3^ 

A X 10 M III 

In all Flaw Xrianglw, - 

As the Sum of the Legs of any Angle,' 
ii to thfir Difference i 

So is the T^Pgent of baU the Sum of 
their o[^o<ue 'Miglet, 

To the Taogeiit of hall their Diflfereace. 

A XIO M lY. 

As the Fafe, or longefl 5ide, 
is (o iheSmaof the ot&t Sidesj ■ ' 

• So i^ the Diffewnce of thofe &4aJ, , 
To the Difference ol tb^ Segoients of the 
Bafe. 

€ A S-£' 'f. 

Fig. 6f. Two Sides, and an Angle 
oppQ&e: to one of thejn ^iv^n i the A^Dgle 
oppofite to the other; rfqijijed. 
EKimpk. 

In the A h c a. 5c*£i? , \ " qair'd the 

PrepBrtim^ 
c.h : 6, i d : : cd ! S/ 6 per-Al, 2. . 
64:8, 22% gc:: iS5»< S, 56^15/ 






40 T£ff Toung Sarvejror's Guide, 
Optratioir. 
To the Ar. co, Logar.cb 6^ 9. ip^Sso 
addihe ^ L-tg.cd.ii39 2. 14^142 

"*^"'* Is, id 22-. 30/ 9.582840 

Sum— Radiuf,=S. ib, 56' ij/ y.^i^fioz. 
fji Gmtirt Scale* 
TIm extent from ^4 ? on the Line of Num- 
> j bur>. 



To 

teachei 

ToS. 



22° 30' > on 
5<-i; j" Sin«. 

CASE n. 



Two S'dM and in Angle opt»nre to one 
of them giveD , ihe third S de rfqnired. 
Example. 

cd=2i39 ^ 
Id the a bed, g Ten cb=:^4 Xrcqnir'db. 
id22%3o'^ 
Preparation, 
Bj Cafe the fitft find the Angle b, and 
kaowing the Argle d, you wili find the 
Angle c to be ici' I5». 

Fro^ortioH. per Jx, 2. 

S, i b : cd : : S, i c : b d. 

S, $6. T$ : 139 - : S, loi : i6/[. 

Of-tation. 

A^caS, Lb 56' ij' 0.0807^4 

a. 143142 

y.99 i5"y4- 

Sjbi— IUdiu8=L"g- bd, 154, i2,2i4S7o. 

r, Google 



■"■■''41:i:''.-oV.'r, 



^Tbe Toung Surveyors Guide* 41 ' 
By Gto ten Sculf^ 
The extent from the Sine of 56° ij» to 
101' J5' on the Line oF Sines » reachei from 
139 to 1^4 OB the L^nei of Numbers^ - 

Note^ That the Sine of loi' i;», is tba 
Sine^ of the Complemeot to 180. d<grees 
= Sioe of 71" 45'. 

■CASE m. 

_ Two A'-gles and a Side g'ven \ the other 
Sideieqdiied, 

ExaiKpJe. 

given, ^id =22.30' reqa..^ 

FrapoTthn. perJxi. 
S,i d :cb:;SZ.c.-bd. 
S.22°.3o':64:: S, iCi 15: 16^. 
Operatiati. 
To Ar. CO, Sid 22° 30/ 0,4171^0 

addthen^^'t'*'*'' S'-99i?74 
I Lig,cb 64 ]. 8a(5i8o 

Sum— Raditis=: Log, bd. 1^4, 12. 214914 

By Gmteri Sculi, 
The wteni from the S, 22' 33'totheSiBe 
101° 1 5' on the L'ne of Sines, reaf hes from 
64 to 164 on the Lfne of Numbtr". 
Proportion. 
S. i d : S, 6 b : : cb : cd 

8,22.30:8,56.1; :;64:l30. 



' ^2 The Toung Suroffj/or't CuiJe, 

CASE IV. 

Two Sid« and an Argle compKhendfd 
bj them, given} the other Angle* required. 

Example. 

Prtftratim hj the third Jxim^ 
cd =1^9 
cb =? ^4 

Sam =cb^-cd =« 2oy; 

Differ, cd—cb at 75. 

Prom ISO* o"=rt«fcfrt^>ftiM«f« Triangle;, 
aibmattioi, ij =to the given Angle. 

R«iniin 78, 45 — [q rfie Sum of theoppofneABgles.- 
,Remain;:^3pa2Jz::iohalf die Sum of the oppofiDe 

FA FOR T 10 N. 

cb-(-cd:cd i.cb::T, A^iiiT.i- X 4A 

aoj : 7Si.'r, 3o"a2' J- -.T, irf'Ja'i 

OPERATION. 

ToAr. cwLog. ed-t-cbj&j ?. iSpajo^ 

Adding ^^''7? 7S _ , I 87S0<i 

J-UbdJ 

!S*r|- 9- 481737- 



(a,;-3Hin ■) f,3?" 

8>m.-Rad— T.iWff. J ( u': 



cy«« V. 



The Ttnm^ Surveyor's GuiJct aj. 

CASEY, 

■ Two Sides, Mi the Angla comprehended 
g ven i the other Side n quired. 

gi«n, . '2cd=i29 Vxeqabtf. 

Prepiratm. 
Find the Angles b d, by Cafe the fourth. 
Proportion, per. Ak 2. 
S,i b : rd : : S Ic : b d. 

■. ^ "6 Operation is the iame with Cafe the 
fecond. 



C ASE.yl. 

f^g.62. The thr« ffi^ea gjven-5 ihe Angle* 
required, 

^ , Examplfp 

In theObl. A b cd Sy f^°57 ^q^j^ed th. 

6'*""- ?cb'=5o ^■'^"S^"- 

Preparation hy ^pra 4. 

From the Vertical Anglf, upon the Bafe-b4 

Let fall ihe Perpend icuUr-^ — ■— Ca. 

Theadic^ E.IC J" U1CD2 i seg«nttjd,ab. 
c d 






44 Tibd Tomi^^ Survejor's GmJe^ 

c d = 70 

c b = yo. 

Sum = cd -f cb = 12a 

DifK = c d — cb =ss 20. 

Troportim per Ax. 4. 
d b : cd ■+ cb : : cd — cb .■ df =s da-b» 
105 : 120 : : 20 : 22,_ 8. 
OptratiiM. 
To Ar. ca Log. bd = 105- S. 97881 r 

Y Log. cd-t-cb=i2Q I. 0791B1. 

Add SLog. cd— d> = *o , o.,3oio3o 

Sum— Ridiin=cLog. df 2^1 8. 10.559022. ' 

By Gmters Scal>.. 
The fH«nt from loj*). 

To 1 2cC On the* Line o( 

Will rfach from acr Kiimbett., 

To 2 2,8 J 

b^=io5=Baff. 
fd =22.8= Difter.S'gmentt, 



Sum 
D 



In 



'in 1 27-8 ; \ 7 

> its T < 6 5 .9=d= < >Segmenf; 

.'fr. S2.ijS /4i.7=ba=>S 
Then the A^-gles are found by Cafe 4(6 
of Right Angled Triangles^ , 
pyopvrtion. 

fn the ^ c aJ> I j^^S. 90:: 41.7:5.76.30., 



The Toung SiirvPfOr'sGmde^ 45 
T .1. ,1 cd-.Rad.:; ad : Sic 

'■"■""^ " ^1 70 : S, 90: : 639 ;S,il5;-,«'. 
^ From 90' oc* 

Suh, %6 ?o. 

Remainders 35, ;0 = i b 
From 90° CO' 
Subflraa ^5 06. 



Remainder = 2 4, 54 = id. 

To 56' 3C» 
Add 65 06. 



Sam =11 21. 36 = i c ina be d. 



Pra&ical X^igonometry, 

W^berthitbe Doffitne 0/ Fhne Triavgltare ap- 
plied to Pra8ict. 

IN thh Sedion, I Ihall trett 6n1y of Ttldi 
Practical parts thereof, as The Dodrine 
of Plane Right-lined Tnanglea becomes 
fu'^tfi'ienr tc ; As 

I. In ALTIMETRIAv Bv which 
the Htight of any ObjeQ acMffible, or 
inaccefliblp, may be found 4 Ai of Trees, 
Steeples, Towers, fiT'c. 

3. In 



4$ Tht Tmng Surveyor's Gmde* 

2. In LONGIMETR.IA : B/ which tTie 
Diftaoce oi one Obi d from soy place, or 
of many Objedi ooe from another, whether 
approachable, or in-approacha^le may be 
known, their Pofitimu Uid dowa, acd « 
Map maJe of them. 

Of Mimetria, 

frob. X. Ofm Jhitttdetbatis Jaxfbk. 

r^. 6i. Let AB be a ^ower , whefe 
Weight you would know. Firfl^ At any 
convenient diflance, ai at C, place year 
Q.uadrant, or any other Inftrument you 
make ufe of, and there obferve the Angle 
■AC3, which let be 58% fo much is your 
Angle of Altitude Meaiure next the di- 
ftaoce between your Inftrumtot and 
Toot of the Tower, viz. The Line 
which let be 55 Yards j then have you 
light Arigled Triangle, one Angle g given, 
and one Lfg CB to End the other AB; 
which you. may do as you wfre taught in 
Caffi. of Trigonometry: For if you ta)(e 
58rrooH>o, there rcmatn9'32 for the Angle 
at A. Then fay, 

Ai the Sine of (he ^ A 33 9.734110 

iBcochc Log.otthc 1. 59740 "] Addrheiwotc* 

Bate CO is >gerher andfrom 

Soi]ttwSlae«fdie<i>G)S 9.929426jrhe Sum Sub*- 

■ • I I'- flraft the firft. 

To 

..Coo<!k- 



The Toung Surve;9r^s Ga/A. 47 

To th« Log. Height of [he "l — — — 
Tower, AB, 40 Yards. Ji. Soai jo. 

■ ■ ■■!■■■ < 

Ta (his 40 Yards,, yon innft add thtf 
heighihof youiIrtAfuincntlromtheGraHnd, 
In this way of takii'g Heches, the Ground 
ought to be very Level^ or ynu may make 
great midalcet ; Alto the Tower of Tree 
mould ftand Perpendicular. 

fVoi. 2. Of a« Abhude iimecefibls. 

tn the foffgoing Figure , let A B 
be the iTo^r or Steeple, and fuppofe 
CB to be a ]™>te, or fome other hindranfce,. 
that you cantipt come nearer thtn C\' plant 
your Infirument, and take the AngleACB 
' J 8 dig. Then £o backward any convenient 
'"-diflancf, as to G, ihere alfo take the An- 
gle aGB 38 deg., Thii done Sabftraa ?8 
?fom 180, lo have you 122 deg. the A'gle 
ACG, then l£2 and ^8 being taken from 
180, remains 20 for the Angle G ^C, the 
diflancs GC meafured is s.6. Kow by 
Trigonometry fay, 

_Al ihaStneof the i A 23 ?■ 5340?2 

utheI.ng.ofthediflanceGC26 1. 414972 
SoiB the Sine of the Angle G 38 9.789^2 

1 '.204J14 „ 
to the Log. of the Liae AC 47 i. 6^0269 
Agiin, 






48 The Toung Surveysr'^s Xjuide. 

Again, As Radius io.oooooa 

Is to the Log. of the Line AC 47 i .672098 
Ho is the Sine oi the Angle C 5S 9.928420 

To the Log. Height of the 7 ii,6oo;i8 
Tower <»o Yards. 3 - 



Bit as I told you before, the Ground muft 
he Level. However, if it be not, I will 
ihcw yoB, ■ , ' 

Frob. 3. Hov to take the Right of a Tower, 
Sec. when tbi Grmni either rifes orfaUi. 

F'g.6^ AB is the Tower, CB the Hill 
vhereon you are to take lhe< Height of 
the Tower : Plant your Inftrumenr in any 
plactof the Hill, a> atC, dirr^ (he Sights 
to A, and fake the Angle A C d ^ which 
let be 19 dg ^o Minutes. Take alfo the 
Angle dCB; which 184?*, 50'i then mea* 
fure the diftance CB 56 Yards, take I?*?*^ 
ihere remains 70° 30* for the Angle A, 
then (ny. 

As Sine 70' go* 9.97454!* 

is to the diftanctf CB J6 Yards 1.74818^ 
So are Soih the Angles at C, 9.957276. 

Mt.6o•■oc^ ■ 

1.7105464. 

:iS. 

To 



To the Heii^loftheTjwer i. 73 

^4 Yaids. 






Tbv Toung SumejiGr^s Guide. 49 
To take thia at (wo Stations, without 
coming to the Foot of the Tower, is no 
more then what has been faid before-, fot 
you .take your An^lea at G, and then mea- 
uire to E, and there in the like manner as 
before, take your Angles again, thereby yoji 
may find -all the Angles, and the Line /l£, 
'then fay, 

Ms the Sine of the Angle ABE 
is to ttie Log. of (he Liue £A, 
So is the Sine of the Angle AEB ' 
To the Log. of the H'right of the Tower; 
AB. 

P- oh. 4. Hov to take the Horizontal'Lms of c 
. Kfl. 

K^. 65. Suppofe KLMN an Hil), 
whole Bafe you would know. Plant youc 
Inflrument at K, and caufe a mark to be - 
fet op at L, ^o high above ^e top of the 
Hiil, as the Inftmment {lands fcom the 
Ground- at K, and take the v\rg!e LKN 
58 deg. Meafure the diflance KL itf Chains, 
80 L in ks. Then fay, 

As Radius 10.000000, 

is to theLineKLi^ 'Chains SoLin. 3.225309 
iSoift theSiHeComplementof K.;8^ 9.734210. 

to p»t of the Bafe KN 8 Cha. 1 2.949'5i9 
90 Lid. — •' 

P Bat 



50 TheTou^ urve^or^i Cwds* 

But if you have orcafton tameafure rhe * 

whole Hil), plant a^ain your loflnjnient 

ar L, (or.M,) and take your Angle NLM, 

which let be'46 d*g. Meafure alfo the di- 

llance L M 21 Ciiaioi: l^en ky^ 

As Radius loocoooo 

Is to tie Line XM 3i Chains 1 323219 

So is the Sine of the Angle 9831:934 

MLN4«°. .. 

To thepart of the Befe KM 11.1791^3. 

Which I V Chains 12. Lin. added to S 
Chains 90 I/'n. makrs 24 Chains, 2 Lin. 
<or the whok BafrKM. 

I suntiomd tiiis way, fos to aake jcm 
tinderlland how to rake part of a Hill ; for 
many times your Survey may end on th« 
Side of a HiQ. 

' But if you fiod 70D avetotake ivtlu 
whole HilU'yqu med not take Co mqcb paint 
as the fofmer way. fe» thus : Take, » bt- 
fore,|he Angle K j8 d«p. MeafureKL-Theo 
at Ltake the AngU KLM 78 deg. Sofe- 
tiraa thofe 1 from 1 80 deg. Reiii8tiK44 
for the Angle at M, Theu fay, 

Aa (lie Sine of the Angle M. 

ittotheLog.Df the Side KL» 
^" So, is the Sine of the. Angle at L 

19 the Lcg.of the Safe KM. 



The Towig Svrve^&r'a Guide* %t 

fVo*. y. Wmtotaie the Althsde 6f an Gb- 
. jfB ^.mding upon a H'lB^ htaccefible. 

_ Pif. 66. Suppofe N O to be the Ob- 
je&, and you ftrnding at P were requi- 
red to find the hetghtti thrteof, ' 

Firfl» upin Paper draw a right Line at 
pleafnre,- as Q.T , and make cfioice of Any ■ 
Point at plealure, as at P, for the place ol 
ywir flanding ; then with a QoadniDr dirw- 
trd ro the Top of the Ohjt&, von find the 
l>gr«eB cut to be 40°. ^2', and tften dired ihk 
Sighrs to the Bottom of the OtyjeQat Oj 
and let the Degreees ciube Hf'.if, ■'■ !' ' 

Then oprn P, prottaa an i (tf 40 ° yi' and 
draw the Line P w at pleafure'^ And an i. 
uf 22'. 2;', anddtawtfie Lim P c at plea- 
fure, 

Secotidly^ Ro forwards in a right Line to^ 
wards the Obj-pft as at R, aia 5 feetj and 
there dirfla your Sights to the top of the "-V 
Obj'fdt at N, and jm. wil7 find fhe degreei 
cat tobe6i*-£2',t}iroiKh|whi(A-drawa line ''-". 
« pJeafine, at R S, croMing the line P w in 
thepoimM, the top of the Ohj^.; Froa» 
vAKXitt a Perpendicular let fyX\ open the 
Gronnd-Un« P T, as KKj that line (hall 
be «gi>al fo ^he AUiiadc and ot the Hi]], 
aird the Objedl together , (cnti Jhea 
the SSgbti to 0, and it-jv tbt Lhte R f, 
■ixn'wg the tint Fc in theyoint 0.) 



53 The Touiig Survey cr^s<juiJe, 

Now by the Inffrfrdions of theft four 
Liiirt. Pw, Rs,P(', Rf, there 18 conftiiuted 
lour Tiiangles, w'- PNK, and RNK, boll 
Itieht Angled at K, and PNR, and RNO 
Obliq'ie apgled ; By the rtfolving oi which 
from the difiaoce (Deafured PR , and the 
ftvttal A':ig\ti nbCetvtdy arRandP, you 
1)13/ find the required Altitudp. 

I. In the OWiqueangJed Triangle PNR, 
Ih^re ij given, the Angle NPR 46*52', and 
ihe Angle NRP ii8*28'i for it ii the Con;- 
plememof the AngleNRK 6i'*82'to i8o'. 
And the Side mejifured PR, 212.5 FooN 
And having (he Angles at R and P, the Sum 
of theinis i;9°. 10', w'lich take from iSo, 
there will remiia 20' $0' , for the Angle 
PNR. From which Triangle given, the two 
oiher Sides PN, aod NR may be fouod by 
Aiioin 2. thus, 

AsSineof ihei PNR 2o'So. 
Is to the Side RP Log. 272 ; 
S) is the Sine ot NPR 40* 12 
To the Side NR 3^0 

And fo is the Sine of the Complement of 
6i\%2'=^ ilZ' 7i>'(ortheLmp,) To the 
biJe PN, 71?. 66. 

In the Right Angled. Triangle RNK 
rtiere is given,C!) The Hypothenufa RK = 
= 80 Foot f2) The Angle NRK«I^3=2d. 
U'lwreby you may fiud NK, by j^afe t.of 
itieht Angle lilain Triaogleii tJ»M\^ 

A 






The ypung Surveyor's Guide. 5^ 
Aa Radius i Sine 90 i. 
Is to the Hypoihenufe NRitSo. ^ ' 
Sa is rhe Sue of the Angle NRK 61. 32. 

To the Sine of N,K 3^5. 
Equal to the Height of the ObjeS and' 
the Hill together. 

And To is the Gofioeof NRK, via. RNK' 
2S, 28 . To (he Logar fide RK, 179. 4 
Foot. 

To which, if you add the meafured d:- 
ftance PR 212. their Sum will be 391.?, 
for the whole length PK, Tht-n, 

In the Triangle FOK, von have given, 
PK*?9i.<)Foo^ andthe iOPK 22\ 2'!.. 
hy which you may find OK, by Ca'e 1/, 
of T'igonometry BR, L, T. Thus, 
As Radius, Tanp. 4.51/, 
Is to the SdePK ^91. 9 
Si is the Tangent 6t the LWK 22'. 2;'.' 
To the Hf ight of the Hill OK 160. 1 9Foi)>. 
Which fubtirafled from 355. the whole 
Height, there remains 174.81 Fott tor tlw 
Altitude of the ObjVa NO. 

Of Longimetria* 

Piob. I. Ho'v (/.'tiding npon mObjeS of 
ahiowtt Hsigbt,) to find the diftmce ho:n 
thence, to fome other remote Objed, 

F^g.^ySippoCe CA to be the Jide of a- 

Fort or fijlwirk 22. 5 Foot h'g^t and he- 

ing upon the P|glform at C, yoiuf-e a 

D 3 Tie., 



34 The Toung Surveyor*! Guide,. 
T'ce, or other Objefi it B, vrhofe diftance 
TOU would knour from the Foot of the 
V41 at A. 

Th:; LinM ABand ACbeing drawn, 3nd the 
he'g'iihof the Wall 22. 5: Foot^fet from A. 
to C, where by your Iiifirument directed to " 
B, you find che Degrees cut to be fl'. 2 s'» 
which AogW lay down; fo have you the 
Righr-argled Triangle CAB, in which there 
It given, (l.) CA, theheighthof the Wall 
2-2. $ fact (2-) the Angle obferved at C» 
.77'-; 2;' Di'g. by which you may find the 
aittance AB (hy Caft 2. of Ri^bt JvgUi 
plme Triat^Uf.') thus, 

As Radius, Tangent 4; Deg. 

To CA, the heighth of the Wall aa-, y 
Foot. 

So is the Tangent of ACS, tfe Angle oL- 
ferved, 7I.25 Deg. 
■ To-the diftance AB, 66. 28 Foot. 

And if you would find the Length of the 
Line CB, you may (byCaje 3 ofR^btA'gt* 
TrimgU) thus. 

As the Sine of the Angle obferved at C 
71 ^ 2;' Deg/ 

Is to the diftance BA, 66. 2tf Fopr. 

So is the Radibs, S'>ne siQ D'$- 

To the Line CB, 69- 98 Foot. 

Fig. £8. Is Supjsofed to be a piece 

of 9 River, and you meafuring along 

one fide of ir, would as well know the 

Breadth of ifv w »Jfa mak« a true Plc^ there* 

■ of. 



The Toung Surveyor' t Guide. %$ 
of, potting down what remarfcable things 
are r«n on the other fide. 

Being at ©I. the firft Station, caufe on« 
oF 3'out Afliflants to go to the next ben4 
of the River, as © 2- and there fet up a ■ 
mark for you j then fee what Angle fioin 
the Meridian ® i- ® 2 makes, which l^t 
be N. W. 6 drg. alfo feeing feveral marki 
on the other fide of the River, take their bea'- 
ings, as the Houfe A which ftands upon the 
Bank, and is a Mark for the Breadth" of the 
River bears N-W. 52 dtg'-ees, the Wind-mitl 
B up in the Land, bears 1^ W. 40 d)g the 
Tree C by the Watei-fide, bears K W 17 
dfg. atl this note down in your Fi«la 
Book, and meaftire the diftance irom ® i ro 
® 2, 1^ Chains, 20 Links. After this conm g 
to. s> 2, feahow the next bend of the River 
bears from you, vhi. ® 3 ; which let be 
N.E.l5f d«g. See al(b how (he Hnufe A 
there bears trom you, viz. S. W. 20 de g. 
,- the Wind-Mill S. W. 50 deg the Trte, 
K. W. ■jj'- -A^^o ^ y°" ^^ gf'irig forward 
- if you fee any thir g~ mere at tliii ftcond 
Station , take tfce Bearirg thereof, ar a 
Aoted Caftle D upon the Land, bears NTV. 
23*, as a Church E clofe by the K'ver 
BrinkN W,4'.meafurethe diftanci! from 02, 
to »3. And p'aciDgyourInflrimentat«3, ht 
Chmch bears irom you N W. 88 d g. 'h« 
'Caftle up in the Land at D you cannot ''«!' 
foi the Chutch, tlierefore let it alone tor 
D 4, .the 



$6 The Touag SurveyoT''s Guidi* 
•lie nexi Station. Bur bete you may ft* 
forward a liitle Village F, (he firfl Houfc 
thereof bears fromyou NW32* deg.Meafm'e 
ihctiiftance from© gtoe 4,andPlaiitirgyour 
Inflrument in ®4,the fitft Houfe of the Vil- 
lage F bears from you Smth-Weft 32(?.and 
iheCaflle D, which you could uof fee at 
the third S'ation, S W. 24* Havirg pit 
down a)] this in your Field-Bock, it will 
be as follows, 

-^.N.W, 6^ 18 Chains 21 Links ,, 
% )ATr« upin the Bank of the », ^ ,( 



S^ River bcirs. 
%ik Wiad-Mill upo 
^= ( A Houfc on the B 



{ 



® 2 N. E, 1!'. i8Ch8ins2p Linkf. 

The Tree N. W. 77° 00 ■) ^hf fc look 10 Ob 
The Hoofe S. W. so 0= t '^ '^ ^ "r. . 

CAOnisfjrnp intheLandN.W. 38. 00-) For- 
2 AChorch upoo the River N.W. 4 ooS-wardOh 
C. Bank ifervitio 



'Aj-^j N.W. ij'.ao Ch. (oLin.T 
■4mc Church Bean N.W. 89 "rThefc look kiok- 
}oThe Caflle cannot be Ceen > ward to Obf. ® 2. 

0?N W^ si.""' ''"'' ^""*' S " ^""''^ '*'*'"• 

0;4. .— 

( The end of the liri'e Village S W 51%"^ Thefe ref- 
«■ The Caflle refpeftitrg ® 3 SW.a. >peflO 3 , 

I, in the Land. S. 24,^ and e 2. 



The Tmmg Surveyor's GuiJe. 57- 
To rntraa tMs, draw the Line N. S toe 
a Meridian, and laying your Protjaiftor 
upon it, the Cencer thereof to © i i againft 
N.W. 6' make a Mark for ihe Line that 
goes to a 2. Alfo agiinft N. W. 17* make 
a Mark (or the Tree,iind againft ^o' and 52" 
for the Wind-Mill, and Houfc , Tiien froih 
© I, through thefe mafks draw ihe Linei 
e A, oB, ©C, 02. Secondly, Trfke troflj 
your Scale iSCoainsand 20 Lin. and fcC 
it off upon the Line ©2, which will reach 
to ©2. , There lay again the Center of 
your Prorra<aor j .the Diameter thereof Pa- 
rallel to the Liiie NS , and make marks as 
ydu fee i;it>ie Field- BiDk,wgiJnflN E !;*• 
N W 77* SW 20*, aw so\ KW28',Ny 
4% and through thefe ma^ki draw Lines, 
the firft Line . direfls to yourthijd Station ; 
thefecond Line NW 77' direa>.you to the 
Tree Cupon the River Bank, for that Line 
cutting the Line i C, (hews you by ihe 
Interfedion where the Tree flood, and alfo 
the Breadth of the River^ Alfo the Line 
S W 20° cuts the Line from the fiift Sta- 
tion NW ?2', in the place where Houfe A 
flood upon the Bank of the River. If theti- 
fdre you. draw a Line from A to C it will 
reprefent'the farther Eink of the River. 
And fo you may proceed on Plottihg, at- 
cording tn the Notes in your Field-tiook^ 
and youwill nor only have a true Plot of 
the Rjver, but alfo know-how far the Wind- 
; D 5 Mill 



58 7h* Totmg Survtyw^s Gmde, 
Mill B, and (he Ciftle D Hand from the 

Water-fide. For if you take the difbnce 
b-Twilt any (woof the places, with your" 
Compaifes, and try it upon the fame Scale 
th« you laid down your Sationary di- 
flances, gives you the diftance required; 

fi'o^. 2> To fni tht diflmca betmeeH awj 
two Placet^ b(ab removed from the Obfenttr. 

^g- 69- L?t the two placet Iw B and D». 
ftnd let their diflancei bie required by aa 
Obferver llandirg,at C, 

I. Let the Angle BCG b* taken, be- 
twefn oqe of the Fisceij as B| and any vi- 
fible mark ^ fuppofe G flanding about tha 
the middle Qf the diftance, and likewife ki^ 
the Angle GCD fee taken. 

a. Then leaving a vifible mark at C^ 
-Jet the Obferver go backwards into another 
Station asatH, in fijch manner, as that he- 
being at H might fee the mark C and G^ 
to a right Line ; and let hini meafurc the 
diflance bctireen the two Stations C9tidH. 

3- At H let him take. the Angle ^HG, 
and GHP, as he did before at C; Thia be- 
ing, done in the Tfisngle HBC, becaufe the- 
outward Angle BCG 'is equal to both the 
ibward and oppofite Angles BUG and HBC, 
therefore by S ibflraaingBHCout of BCO, 
there wi31 remain the Ang'e HBC. ThlM 
all the Angles io the Xriaogle HBC, and 



The TbitHg Satvsyor^s Guide. 59 
iheit^HC iMing given either of ^eothtr 
ttvO'Ades are found by the third Cafe ht 
Plwe Triangles-. 

. Agiin,' in the Triangle KDC, ehe Angle 
HDC, and either of the fides CD or HD 
may t>e found in the fame mannen 

Lofily^ In the Triangle BCD, the two 
Sides fiC and DC being found (as is 'alrea- 
dy tatisbt) ani the Argle BCD, by Obfei- 
vsh'on , ..thti other two Angtes CBD and 

'£Dfi, may be found hy the fourth Cafe 
of Plafie Triangles, and cnnfeq'fcntly the 

• Side BD by the third Cai'e of PlaniTriangles, 
MFhicb is the dillance required. 

0f Leveffin^y or Meafuring the Ine- 
' ^aSitjf iff flaces^ as to their Heights* 

Fig.'-r^O find out the difference of heighrs 
. 70-, X of oiKplace from another, in.the- 
rificg and faUiag^ which is of conftant ufe 
in cwve/ing, ot Water, either above the 
GroHad tor i^ountalns, fJfc. or under the 
Grotvd for Adyts or Soughs, (^c. Let 
Jiout Inflrument be carefully made, »jirhe- 
ithexitbe a Qjisdrant, Water-level, or ang-.' 
ether ', thR befl I Account to be a bra& T. 
fitt fights upon the top of the T, to be Per-^ 
fpe^ive Glafles, which mull be tried before 
ttfcd^ and tbe Gla^lfs are to Hand alw^s 
«iK w&j^ tluwill eodine longer SiatioBs. 
thao' 



The Toting Surveyor's GuiJe. 

1 ordinary, and is for many reafoni the 

I, it fubliantially made, and there muft 

two maik Boards placed upon quarter 

M, that yocr Afllftants may lift them 

her or lower, as ihey (hall be direded. 

Then fet the Level at near at you can be- 

xt the 2 Marks which your Afliflants 

1 upright in ^eir Hand*, with the flip- 

; Marks ; turning to one, caufe him to 

d or fet the Hit and Black firoke enn 

1 the Level fights, and fo the othirV. 

difference of thefe fights, in Inches and 

1 parts gives the Afcent or Defcenti 

his is^ ope fimple Station ; but if it 

res boihAfcenti andDefcents, then in a 

fct down yoor Bark Stations in ope 

nn and you fore Stations in another, 

ip boih the Columns, and take th'c"dif- 

e of ihemi if they be equal, the two 

art Level,if your foreStationeiceed,the 

nee IS lower, if olherwife, higher. Atl 

lie will clear all. I am to give the 

ice of heights of the places A and B, 

ie Line of the Level -SB, chufirtg my 

)tion at C, where I plant my Inftru- 

betwir, the Quater Pikes A a"<*_JP, 

ing my Level firm, (he Affiftah's 

ip and down the mark Boards till 

ys the fights take the Black (IrokfS 

id E i in a little Table rnade, fit 

e heights of ihofe flroakes from the 

in two Coluninis, one for the left 

HatJd, 



"The Toung Surveyor's Guide. 6i 
Hand, the other for the Right, as you fee in 
the Table adjoining, \wbereiri AD (for the 
lefthmi) J8 found (6 be four Feet three 
Inches 4t of an Inch, aad EF (jor the right 
Hjnd) feven Feet, 1.5. 

Again, Let the Second Station be at G, 
and the left Hand height FH be ten Feet, 
(hiee Inches and a half, and the Righl-hand 
height I K three Feet, 3.7 Inches. Again, 
The third Sation let beat M,and the Height 
IL 2 feef, 9,4 Inches, and ON 12 feet, 1. 5. 
Inches. Lafily^h-t the fourth Station beat P, 
and the height OQ three Feet i o. 9 Inches, 
and BR 1 1 Feet 9, SInches. The Sum of the 
heights on the Letth^ttis 212 Feet and 
three loches, that of ihofe bn the Right 34 
Feet' aiid 4,-5',Iiichesi thriif difertfice is 
1 3 Feet and i', S Incbvt and fo much is B 
Jower then A. 



Stacions- 


(fcightionthc 
Left-hand. 

Fecc- tn. 


Heights oD the 
Right hand. 




Feet. Idchci. 


I 

3 
4 


4- 3. a 
10 . J.J 
3 94 
3 10.9 


7 ' tS 

,1 11 

11 PS 


, 1 21 3.0 


u 4.5 



Sumot thcHights on the Bight hand 
Sara of the Heights on ihc lett-bind 



Their Differ. 
And lb much is Blower then A. 



6i The Ttung Surveyor's Guide, 

I The TJfe of the Line of Prdportion^ or 
HJumbers commonly cgUea Gunter's 
Line* 

TH E Irg-nious Mr Qmter anJfeverat 
othen have fufficiently handled this 
£ub}ed, thereforei might have Taved my felf 
that tloi^lc% bat becaule it wilt be ezped 
ed here, and the Book more aferul^ I (hall 
lay fomthirg io that purpofe^ and begin 
ficft with, 

X^oratioK upon the Line. 

Kaineftticn. by the Line ^yb^undefr 
fiood from this one Tfaougt^r, is'z^ That 
what DeoominaMpn foeve r the £ift at the 
begituuQg of the Line is, that in the middle 
will be ten tiiUfB, and that ac rTie end will 
be an hnndred (iipeB- fo many : Which if un- 
derdbod, it will [not b.e difiicutt to know 
what the imiermediate Figntes aod ' partt 
are. 

1 Example t. ^ 

To find the place of 25. you may call' 
the I at the beginning or the Line, hut 1 
' t , th«n will that in the middle be 10, and 
the twa which {lands, open the xi K.a- 



n 






The Toung Surveyor's Guide. €^ 
£i-it^ will be 20 j then count five of ih« - 
grand DIrifions) where ftop, for Et hat ir 
the place which reprefenta 1 ;. Where note, 
that if you had efleem'd the i at the be* 
ginning of the Line but I, that is, on« 
vtenih, the place which now reprefenli 25,' 
would fignify but 2- ; : Alfo ii you had 
efteeni'd it as 10, then would the place .of 
25, be 250; if iQOj then 3jQQ,if but cut 
then but 025, ^c. 

Example IL 

To find upwi the Line the the place of 
^6;^. Firl), e&^em th« i at the btg^nning 
pf the Line to be. xoo , theniwill ihst ia 
the middle baioozt^ndthf MUMitpwfiF^th^^ 
niiddle joqo. ; from which count fix of th« 
6rand-divifioM ind a half towardt (4000) 
and then you will come tp the pVace ot 3(5 50. 
i^ow you mitft itoagine the 2 10 be % little 
beyond that half (livifipm for in tbia and 
the like examples," whffl^e wre are tp find ^P^^.^ 
places, that which \% Utjiiei n^A bf takei) 
by eftinution. Sa have yoa the place 
■ 7652. ■ ' 

Note^ 'By thefe Examples lad medtioned, 
. yoq inay perceive that tlM ^igofeii I, %, 3,4, 
F ?,'$, 7> 8, 9i do fomttiiaeifiigiif/' theiB- 
\ felves aloM,. fonistijttMS la,. ;ao,'. jo,' fc, 
^ i£Knetiin« iqq^ 300, goo, Q^c. 4.3 the 
vork peiformi'd thereby Ihall require .-The 



(>4 The Tmng Survejior's Guide, 
firft F-'gare of every Number is always that 
which IS here ftt down, and the reft ofthe 
Figures are to be fujiplied accordiigas the 
^aeftion (hall requirf. And by the varia- 
tion and change of the power of thtfe Nain- 
bets fromi, to lo, or loo, or io"o, any 
proportion, may be wrot'g'it by this, 

■ • General Rule. 

Always extend the CompalTfS from the 
UtR Kamber to the Tecond, und ihat di- 
ftance, or extent, applied the fame vay up- 
on the Line, (hall reach fron; ihe third to 
the fqutth Number reqiiiFed. 

Or other*iftj' extend ihe Compailes from 
the fiFfl'NDlrtlW#W>'the' -third,' and that ex- 
tent apjilied the' ^ittieway, fhall atfo reach 
from the fecond to the fonrth. Either of 
thefe ways will effeGt the fame thing , as 
by Examples following 0iall be made ap- 
■ e^t^^An'd it is neeeffary thus to vary the 
roportion, fo as to avoid the opening of 
the CompilTes two wide; 

MttlcipVcatioK iy the Line, 

This Rule whether it be performed ArJth- 
meiicaily^ot' Ipftcumentally, depends ap- 
on EurJids. El'm^ P'op. i. lib. 7. where it 
is demonfirated, that if two Lines be pro- 
posed 

r, CoO^k"-' . 






The Toung Surveyor J Guitiff^ S^ 

pos'd, whereof one is divided into diverfe 
parts^ the Re^anglp contaiijed under thofe 
(wo Lines is equal to the Reftangles con- 
tained under the Line which is divided, 
and the pans of the Line divided. 

The propoftiDn it, .as one i& the Mut- 
tiplyer:~-So is the MuUiplicand to the 
Prochift. 

Example I. , 

Let it be required to multipljr 8 b^ 7 
-the PifopoHion is, a»r: is to 8 :: fo'is 7: 
to $6. Therefore' eitend the Co'^paffes 
ttom I to 8 i the fame extent will read) 
from 7 to s^, which is the pr odud. 

Example 11, 

■ Let it be required to Multiply 37, by 5 
The proportion is j As 1 ; to 5^; (6 is 37 '■ 
to iSj^ 

Set one Foot of the Compafrfs in I, and 
eitend the other Toot to S ■■, that fame ex- 
tent will re»ch from 37 to 18^, which is 
the produft ' or 37, being Muhiplied by 
5. Otherwife, fet one Foot in 1 and ex- 
tend the other to 37 •, the fame extent will 
reach f[oni 5 to u; 



ExampU 



6 6 The T9ung> SiiniejKr*s Omtte^ 

Example III. 

. Let it be required W multiply 8. 75 by 
3. 6. The Analogy or Proportion is, a* 
I. to )^6:: So is 8. 75, to p.$. Set one 
Foot in I, and ntend th> othtr to 3. £; 
the fame extent applied forward upon the 
Line will reach from 8.7; to 31. ^. 

Diti'j&K by the Line. 

. In Divi£on, th^ Qaetient contains Uni- 
ty as often as the Dividend does the Divi- 
(oi : It follows (hen from the <;th Dciini- 
tioD to the %ih Book ot E«cliit Element^ 
that the Quotient is in Propeition to i, 
as the Dividend is to the Dbifor. From 
whence we may deduce the Proportion fol- 
lowing, viz. As ^ Divitor is to Unity, fo 
is the Dividend to the Quotieot. 

Example 1. 

Let it be required to divide 40 by S. 
The proportion is, As 8 : to i::4o:5. 
Set one Foot of the CompaiTes in 8^ and 
extend the ocher Foot to i ; that fame ex- 
lent will readi from 40 dowavardsto ;:, 
which is the Quotient.- 

Otherwife eitend the Compaffes from 8 
1040 i the fame extent will reach from i,to^.. 



Example II. 

'' Z-ttit be required to divide 356 by 12. 
The Proportion is As 12 ; i ;: 3?6 : 28. 
Extend Uie Gimpaflei from 12 to ^j6 j 
the faitie atent will reach from I to 38 ^ 
which is the Qiiotent required. 

YquI know how man^ Figares Ihould" 
be in the Qnotient, by fetting the Divifot 
ordetlj.itoder the Dividend, &c. 

The- Ruli of three hy the Line. 

The Rule of three by the Line mull la 
performed by ths Jafi General Rule^ 

Example I. 

If 3$ Acres of Land be worth ^4 Z. « 
YiWt\ what IB ;5 Acres of the fame Lind 
-worth by the Tear. Proportion as s6 : ^4: L 

So 36: to 88. 6\p 

Extend the G>mpa£les from 26 to i54, the 
fame txtciu will reach from %$ to 88, 61 
which is 88 i i 2 J. ^d. 2 q, lot the Anfwer 
of (he Queflior, 

To esOraS the Sipare Root by the Line, 

Divide the fpace between Unity and 
the given l^iimbtc into two equal parts l 

* . Where 



^ 



68 Th/t Taung Surveyor's Guides 
Where ih^ DivifioD fallg, is the Square 
Root fought. 

Ev ample IT. 

To find the Square Root of ^$. Ei- 
tend the Compaiies from I to 3^, the 
Middle way upon ihc Line between thefe 
two Numbers is ^, which is the Square. 
Root of ?6- In like manner yo<i mSj^Sd 
the Square Root of any other Nimrt^B^ 

Of Meafuretn£, , 

A clearer Idea of which youcknnol have 
than that giren by the Inge'nioi^ Mr Cnm, ia 
his eictllent T/ealife of Fraaioiw complea- 
ted, which is as' follow. 

Every Magnitude i$ meafiij'd by fome 
Magnitude ot the fliine: kind, a Line by a 
lineal Foot, Yard, Cft- 3 Superficies by * 
fquare Foot Yard, £5'c. a Solid by a 
Cubicle Foot, -Yard, tfc. 

The Lkeal Mgajiirc ishnamtoaU' . 

The fuperficial Meafure may be concei- 
ved, by imagining a Floor pav'd wirh 
Tilea, each a Square Foot^; for then the 
N unber of T.lts is equal to the Njmbfr of 
fquare Feet in that Floorirg. Now if (\\s 
Flooring be juft one Fpot broad, the Nuin- 
-. ; , tier 



The Tomg Surveyor's Guide* 6^ 
ter of Tilts (or of Square Feet) will be e- 
qual to the Number of Lineal Feet in the 
Length of the floor ^ hut if the Flooring 
le 2, 3.-4>~ 5. tP'c, Feet bload, the Num- 
ber of TileB, or of Square Feet, will be 
twice thrice, four times, five tlmei, Vfc, Co 
many Tiles Qrr Sqnctre Fea.) So ii the FJoor 
were It Foot long", and 7 Foot broad, 7 
tifliCB -M Tilei (or Square Feet) ^iv^a 'yj 
theNumber of Tiles or Square Feet in that 
Flooring. 

The folid Meafure may be conceived by 
imagining a Wall buiU with Srone«, each 
a Cubick Foot j then the Number of Stones 
will -be equal to th. Numbrf of Cubick 
Feet in that WaH. Firft therefore,' if the 
Wall be one Foot thick and one Feet high, 
the Number of Stones (or Cubick Fset) will 
be equal to the Number of Lineal F«t in 
the length 0/ that Wall. Secondly, If the 
WalJ ihoald be of the fame length and 
heighth one Foot as bef re, but-the thickliefa 
2, 3,4' 5, f^f- Feet (htftead of me Foot) , 
, then the-Number of Stones^/or Cvhkk Feet'^ 
will ccctdinglyhe twice,ihrice,fourtirnesfive- 
limes Cc. and as many as before. Lafily^U the 
length arid ihicknefs be the fame as in the 
laft fuppofition, but the- heigKt (irflead of 
one Foot) be- 2, 3,4, S Feet ; the Number 
of Stones {or CMck Feet) will be accord- 
ingly twice, Jttice, , four^times fire timej, 
• Ce. what it Was in the foregoing. So if a 
Wall 



yo The Toung Swveyor's Guide* 
Wall is feven Foot Jong, three Foot thick* 
and one Foot high: From what hu fce«a 
(aid, a Wall of fet'cn Foot long, one VoOt 
thick and one Foot high confifts of feven 
Cubicle Feet -, bat a Wall of feven foot , 
long, three Foot thick, and one Foot high, 
cotiAAs of three rimfs &v?n* Cubirk Pert, 
thatis, ziCubickFeet. Lafiiy^ A Wail of 
feren Feet lone a<nd three Foot thick as be- 
fore, but five Foot high, cciitains five rimei 
as many, thar is five times s i Cubick Feet, 
or 105 CubifkFeef. 

'From all' which is evidenr, that in caflif^ 
up any Menfuration, iha Multiplier iq an/ 
of the Mslti^licaticuis is an Abflra3 number 
. BSiyellasinalt orfaer Mullijilicdlions w^at• 
foerer, which may prevent the talfe Gonfe» 
quences ufually drawn from multiplying 
Feet by Feet, »/«. That of multiplying by « 
contra^ nu mber,as 3 /. 1 9*. oi-hj 3 1 ; 1 9 / : or 
Half aCcown by half aCrowni which is con- 
trary to the Nature of Maltiplicatfon, whofe 
Operations are wily compendious addilions, 
cither of the Maltiplicand or fome part of 
it, <ontiDualIy toitsfelf or its part., 

Suppofe a Roof' in length 120 Foot on; 

both Sides, And the depth of one Side 18 

foot jthefe two numbers multiplied togethjfr 

]^odcce 2i^ofoot,whicbis 21 S^uareff,and 

- 60 . 



Thif Tmng Surveyor's Guide, 71 ^ 
fioFoot/fhalis, lo Foot above half a 
Sgoare more , it being maaftir'd by tbe 
Squwe nf 10 Foot every way^ fo that 100 ^ 
Square Foot is one Square. ^ 

Brah, I. .To meafure a Qeometrical, ortrae 
Sqttjrv. 

Mulriply the length by the Breadth, and" 
the prodo^ ii the Area (hereof. 

Example 1, 

Fi]g.7i.AdmiiKLMN,whore fidet is 5,which 
Mulriplied by ?, being both the' Length 
and Breadth, produce 9 for the Area^ ag 
may be %n by the Sdume 

Froi. 2-' To ^eafiife » Ing Squtre or Parah 
lebgram.' / 



Mhe 



Muln'pljT (he length by the breadthj the; 
product is the Area. 

y Preb. 3. To meafim a Rhomhft. 

Is is dcmonAiated (hj the gtb Theorem) 
thatParallelograois having the fameBafe^and- 
being between rlie fame Parail?ls are equal, _^ 
tAthat the Parallelogram A6DF is equal to thtugVl^ 
Kbombua a b fiF ; therefore if you intilri. 

ply 



The Toung Surveyar^s Guide. 
\y BF one of the fidrs by OF or a k the 
'erpendicuUr , the Produd will be the 
Area thereof. 



?: 



Examol^l. 



Let at BF be a Rhombus, whofe fideBP 
js 40 Inches, and lei the neareQ dift^ince of 
any two oppofite fidfs, which Uthe Perpen- 
dicular, as ak = AB be 34 inches, Z de- 
mand the Area. 

Multiply BF =40 
by DFxfH 

Anfwer. 1360. 
Trob. 4. To Meajare a Triargh.- 

TheParallelogramBACEis double toA ADE 
0)y Corrol-S*Jl)eoremr- lo). Therefore Mui-. 
tiplv the Bife AE by half the Perpendiru- 
U% DF, and the Produa is the Area of the -^ 
Triangle ADE. 

Example I, 

Let ADEbea Triangle whofe Bafe AE 

= 2o, and the PerpendicuUr DF = fe,^ 

what it the Area. ^-^ 

Aafwer, 80. 

ProK s* 



VrtAlm ^. j 

To' imafwB ia Triangle , tlie j 
diree Sides ht\<o% given, wiliioat nndiDg tbe \ 
PerpendicuIaF. [ 

-R V t B. 

Add tcgether all the three' Sides ; 
ud from 4 their Sam fubfirad every fide, 
which call the three DJfTeremes % Multiply 
thefe three •differences, and the ^ Sum con- 
tinually tpgether^ the Square Root of rhll 
)aft produ^ ii the Area thereof. 

' Having divided the .T-rapezium in- 
to Triangles as the Figure following, add 
the two Perpendiculars, viz, AB.and CO 
. together, and roultiplj that Sum by 4- the 
Bafe LK, and the fteaangle oi Prodti^ 
it the Area. 

" ".'"^jBvinMpfe. , ■..-... 

Tig. 74. Let.6iLDKbcaTrapn!iuin,le»' 
tlie common Bafe KL be loo Inchei, the 
PerpeBdicula?~AB 40, and CD = 14,1 
demand the Af^ _ 



7+ The Toung Swrveyor't Cmde, 




3700 Anfwer. 
Rrob. 7. Te UStjfvrc my fi^sLir Fo^off. 

F^. 7^ Multiplj. the Sum of all the Hdes 
by 4. the ^ifiaoce of any fide from theCen- 
terj and the product ii the Area, {or they 
may be divided in as many Triangles as 
they ibaV« fid^s^ aod tbofeaill .tquml to one 
BDother. 

■ Etmk^. ■ 

Let ABCDEF be a Hexagon , any 0} 
whofe fides it 10 Inches, and the DeareR di- 
fiance. from the Center to the middle of 
an^fidfl i* $. 4'Iiich<ss whu's the Kxv^ 



Multiply the Sum of thtTidci =: 69 
MlUlf^fcrfCBdiaiIir = 4. 7 



383. o. Aim: 

fi-oi. 7 



The Tomg Suw^r's CuiJe^ 75 

Every Circle ii equil to thai 
. OUorg, or loi^ Square, whofe Length is 
Mjjal to T the Circumference and Breadth 
rtjaal to it< Semi Diameter. For a ( ircla 
ja a r!4g^rPoI]'goa,h»'in^an infinite tiBoi- 
. bejfof fid«4i.aiW Aerlefpre ihe Semi Kame- 
ittt IS elyvays .f^ttpendiculir to ^oOe of> iti 
fg^i. rWfee«*ifflfe. maltiplT- 4-' ^^ Circnm- 
((Sence^by i» Semi^Diameter, and the Pio 
jduS ia t« Ares; thereof ^ : . 

'to !■ ^: ... V . - ? . .-; iiir'clf. ' " ' y-'-.' -' 

Every Circumference ia more than 
TripU ,tb*H, D»met5t4 bw the.meareil 
i'ational Nopiber, ketwjfen the Diameter and 
ihe Circumference is, as 7 to 22. Th«c- 
foietf-Joii BfcuJ(ii5)tjt^^'tTi& D'anieterby as, 
and divideth^ Pcodwn;<b|^ 7,-thQ'Q(iotieii« 
viU..f^^ fciktte £irL-ii)rifn:ence. 
idWatc'^EVery Circle ia equal to a Re^. 
■dgle'Tsi^ngle, one a£. ivhofe Legs is the 
Ra^UB, and the other Rigbt-liRe equal to 
tnt Circonjference of rhe Circle. 

'.StoewfigreiftiijrQiiinaUlliljt; the Diameter 
ty, ^ part of the Circumference, the ^^ro- 
^oA^Ulhe Aieai - '^'i " ■ ■ - 

^I ., '-■ ■...'&» Othef. 



■y6 The Toung Survey^J/GuiHe, 

Otherwife Tqaare iheCianKtar, and mul- 
tiply that t>y It, and divide that prodn^ 
by J 4. the Quotient it ibe Area. 

^ob. 10. To fnd the htifth of mt Jrcb-Lim 
of a CircU GeemttricaBy, 

Fig. nS. Let A BCD be the Arch-Lint 
gven, «h:ife Length \» rfguim).: Firjli^ 
£>iaw the Chwd • line J^, which ilwayc 
divide into 4 equal parts, rtK» take one (^ 
. tho(e parti, and fet it fromO to C uponthe 
Arch- Line : Thii done, draws Line ^ro^l 
the pomt C, to the fitft iDivifioo, which let 
be Ki this Jioe ai ^ the AtchLioe AB 
CD, which doubled fltaU be the length «f 
the Arch-line required. 

Broin IT. To fni tbetaiffb df tn JfrfA-ffiw, 
grMer than a Stmi-Cirele. 

Til 77. F'lrfi, Divide Ae tatd Arch in- 
tQ two <^ual,part9« a> DK } then divfdt 
the Chord-Jim AD, into ibar eaual paitsi^ 
then-ai before draw the Line OP, which 
Line being taken foortimet, u equal to ih* 
Arch.lioe aDF. v. ' ^- 

^ob' n.' To' Metfttrt tht Far^oinf » &t^ 

Fig. 78! Every Portion of -a Ciicle^ 
whicbcon'aiaed uniet'two Stmi-Dianieteri, 

and _^ 



TlieTotmg Sttrv^or's Gmds, 77 
apd one Arch-line is equal lo. ihat lorgT 
Sqtare, whofe Ltngth snd Breadth is equal 
to rhe S.'ini-Diaoieter, and i- of the Arch- 

To find the Center of that Circle where- 
of the Archline ABC is a pSirt of the Feri- 
ferj. 

■ ■ ^ RULE. 

Multiply ;. the Chord Line, vis, A B' 
by itfeI^ then divide that prodii£l hy the 
.Verfed Sine BK^ then if you add the 
Verfed Sine to the Quotient, the Sum will' 
be the D'ameter of the Circle belonging to 
the Segment. ACK j and half thereof wiD- 
be the l^eini'£)iaineter AD. 

Bcample. 

Xet ABC be a Segment of a Circle to be 
mwfared r ; Now it is not at the fitfl'inrlud- 
ed with two Seml-Di a meters j you mnft 
therefore find th« Caiter D, whereof the 
Segment ABC, is a part of the Perifery 
by the laft Problem} then draw the two. 
Semi Diameters AD and CD; fo fhall you 
include the Triangle ACD, inore than the 
Segment ABC, Now firft meafare rhewhole 
Figure ABCD by the^afl Problem j then 
meafure the Triane'e ACD, and from the 
Content of the whole &aor AECD, fuU 
. E 5 ftraft 



73 The Tcung Surveyor's Gvide, 
flrafl \U Content of ihe TtiangU ACD. and 
tilt Rpinaiinier is the Area of the Segment 
ABC. ■ ° . 

The Operatiou, 

Take \ itfche Arrfi Line-. , The Perpendlcn. ED S-* 

ABC 1* iheSerai diwieKr./L TJw Bi(c AC t$ 

8 ; of [fac Arch. (J - — 

Sub.sd.^Areaorihf'riUii^. jf — -> 
r 'Tike ;- 71. » 

HTbe Atttof the a*.* 
Triiade A CD. 
. ■ ■' 

You niay . jreafnre the Segnunt 
ABC, by- multiplying BE by \ of AC» 
and it uriU do well enough iat common 

Praaice. ' 

froh. 1 3. To Meafvn an ESp^y Dt Ootk -_ 

R U ■ i' E.:'' \- .' ■ ■■' , 

Multiply the longeft Diameter, hy tfit 
(horteft, that produft by, ii, andt^di-- 
vide the whole mpdaa by jf, whielj,i U- 
the Area f eqtured. ■ ' ■ 

Froh. 14 



Th* Tmtng Sunejor*s Guides i^ 

pro J. 14. To Meagre the Saperfitial content 
of « Sphere &r Ghbe. 

k U L E. 

Mg: 79. Multiply the Diartieter ty ihe 
Circumference, theprodufl is the Superficial 
Content of the. Globe or Sphere. 

Example. 

Let A be a Globe , or Sphere, whole 
fep(?rfioaVConffnr', or Area of the fur/ace 
K reffliire^ r ! ftiuUipIy the Girctimferenca 
(mhtcbkgiitted'hjPr^'UmS') ^^hyihb Dia- 
meter 14, the prodndt it 6t6, the faperfi-^ 
citl Content of the Sphere reqjired. 

Froh.JS'.'-'Ta Mea/ve the Superfciei of a 

.{, ■ ;... Cow?. 

' ' R ^ir L E 

Multiply the flam heighth fey ^ the Cir- 
cumference at the Bafe, the produfl is the 
CcaHcrf^^Sutface i t* ivhich if y<)a add the 
Area of (be iCifcle At tfle Sa^, you (halt 
have the whole Superfidai Cflntent- 

_E 4^ Pioh 



, eft- The Tbtmg Swv^foi^i GiaJki^ 

Pr(£, i^. To Meafure ibt Stpnfduaf tjh 
Fraftram of a Ccue-, 

RULE 

Add the grfarer and lefler UrcutnfereiiCB 
oflheBafes together, ^ the Sum of whicfi 
Multiplied by itftheiglith, producu tlu fu- 
perfcial Cootent of the Fruflruin. 

Fi. So. Let BCDE he the Fmflnim or 
part of a Gone, the Superficial C«it«itihrre- 
of is legtitred, the Ciraimference pf the 
greater and If&rBafe being 6 and 3, which 

added is 9, the 4. ii 4. ^, which 4.1! maltjpji- 
«dbv i2,theheightbBD,ihefffodu<^ is $4 for 
the tupeificislContent ot iheFrufiruniSCDE. 
ittrfff, The Superficial Content ot a Cy- 
lender, ii found by multiplying the Gilt . 
by the heighth. 

Jnather ^jy^ 

Firft ftod the length of the whok Gme 
ADF, whereof AeFrufiramBCDEiia paitt 
then having the whole heighth ot the CuDe, 

mrafufe the. Superficies by the i-stft, /Voi. 

then meafore the Supeifides of the top parr^ 

or IcCex Coite, by the 'fiinie Problem, and 

fcb. 



The TemgSarvritr's Gmtte, 8t 
Subftraa the Cootent of tbe le0er Cone 
tirom the Conteot o£ the greater ; and the 
Remainder Qiatl be the Cootent of the Vi:^ 
QxJUA 

r B.aS MB Jd XTO. 

The Fruflrum Bf DE given ' tt> 
Xnd AD tbe £d« o£ tile Cone Ulongins 
to it. - 

S OLE. 

Multiply 1^ by BD, slid divide the ptA*. 
dna by PE — BC.the Qjiotient is Al> 
ibught. 

Multiply DE = « 
by BD = 12 



which divide 72 
by DE— BC = 3 
lli> Quotient ia AD = ^ 

tSOB ZFlt XVIIL 

To Sad theSapeificial-Cattent oE.de 
Segountof^ Sphere. 



82 The Tomtg Sunny^^t GuiJe, 
RULE, 



Multiply the Heighih by the Crfciiin* 
ference of the Sphere, (0 which ptoiaQ add 
the Area bfitt Ctrcu^lu B^/oMlhat Sato. 
is the Area fought. 

Prob. ip. 70 Meafurg dCuU. 

^.''■*;^, 

Cube the Side : That is, ipulfiply the fide- 
of the Cube by it feff, and iftirptodbft a- 
gain by the iide of the Cube^ Mrhidi Cube- 
aumbex ia the S^lid Content thereof^ 

''' Tig. St.- Lrt ABqSJEFG reprefent a 
Cube J whofe Side let be 30 Inches j Ide- , 
Hund the Content. 

MlJtiply. one £d^. ^ ?o . 
• byit laf -=' 5io,': 

which produdt HwltspJy yoo ■ ■ • .' 
again by 3* -^■-■ 

it prodnDe£' 2t<3oOi Co^t•■^ 



TBe T^uag- Surveys Gutde* 83, 

By the Line of Ntmhers. ■ 

Extend the Ccmpsfles, .from i, to 30,, 
the fame eitent will reach from 30 to poQ^ 
and from thence to 27000, the Content. 

Pfob^ 20. To Miofure a 'SjralUl^ipedoni 

^R Viz: 

Multiply the Length by the Breadth , 
^ aqd, the produft by tfle £>epth ^ whieb 
gives you the $alid Content. 

Example. 

Fig: 82.'Let ABCt)EFG, reprefent a 
Pai^lelopipfdon 1 whofe length AB is 4a 
Iflcbei^ the breadth BC .== ^o Inches, and 
Depth CD = ly ; what's theConteot. 

Length = 4a 

Breadth = ^o • 



l2Qa 
Bepth ij 

•op- 




-J >8q0O;= 


^ConKnf. 




«<»,xr: 



^4 TIj* Toang Survejior't Culde* 

^oi, 2 r. To Meafve m QUbt ei SgCere^ 

To find tfie Solid Content, thcre.are €l~ 
■Vital vrzyt. At fTtft multiply the Cube of 
the Diameter by ir, and divide the produft 
by 21^, the Quotient ii the Solid Content.. 

2. Ot muhiply the Diameter, bj ^ 
part of the GioUs Superficies, the prodoa 
IS the Solid Content : Or one' fizth part of 
the Diameter muUiplyed by the S£herei Su- 
perficies gives the ^ine^ 

3- Othetwayi, Multiply the Area of 
the Circle, whofe Diameter is cqial to the 
Globei Diameter, by -J; of the Diameter, the 
produQ is the ?olid Content : Or, Multi- 
ply the Diameter by -f ol the, Circlei Area,. 
prodDces the fame^ 

Trvh 22. TofuitbeSoUdCtnte^efa-Cotte^ 

RULE. 

By 9 h'oh. (btf going, find out the Are* 
fjf its Bafe, and multiply that by ^ of ita 
heighth, and that produdl is the Solid Qan-- 
tent ofit^e Cone rr^uired. 

Example. 

There is a Cone, the Citcomfereiw* of 

whsfe l^le ii 22. i % and its heighth is tS.. 

1 demand 



The Tomg ^mij/nr'sGuiJii 8j 
t denaild the Solid content of fiich a Cone. 
A? 32. 

So is 22. 5 the Circomference of the Bafe. 

To 7. 1 « the Diameter of the Baft. 

Then Ihultiply i M. '. "hkh in 11. 25^ 
by i 7. lS2«rhich is 3- 58, and it produceth 
40 281!, »hieh il the Superficial Content of 
the Bali. Again, molriply If-. 286 by u 
333, which is f of the Heighth of the 
Cone, and it produceth 2i4.a4«i;7i the 
Sniid Content. . , . . . „• '■ 

But here you are to obfcrve that the flanl- 
ine fide of the Cone is not to be «ken foi 
its true height, but a Perpendicular let fall 
torn ite Veitn.to it. Bafe 18 ila true heighlh , 
and the fame ia to be obferv'd iB the. Py- 
lamjd- 

ftoJ.. 23. Te fill lis Mf Caileirt of » 

Betureenthe Cone and Pyramid, this is 
theDiffettnce. As the Cone hath « C^cnla 
Bafe, the Pyramid hath a tight-lined Fl?ure 
for ill Bafe,' fo that its Bafe and SopeificiM 
are Ansuki , its Vetiei tenninatii« m a. 
Soiot^ 



9S 7%t Totmg SurviyorU OuUe^ 

MULE. 

Fkft, find the Sapeifkut Content of ihe- 
fiafe : Thes nwltiply that by -f of (he 
Heighth } ami it pcodHccth the Solid Couku 
of me Pyramid. 

IVofc 2\. Tt-Meafari tbt Frujinim of a Pf^ 
iamid or CoK?. 

Fig. ftj. The Fnifirum here given to be- 
neafared u ABCD, tht £de hi (he greater 
Bafe A, being 34 laches, and the fide of (he 
^eSkt Bife at B, 8 Inches, and (he length of 
it I M so Fee* = BO: = CK 20 Foor. 

IC is evident .that if i find the Solidity of 
the whole Pyramid aED, and alfo the Sc- 
lidity ot the leffer Fyramid BEC, and thed 
Aib&aa the Content of BEC, from thp 
Cohtfnt of A ED, there will irenuin 
rhe Solidity of the Fruftrtim ABCD j and 
certainly thii way of meoTuring the Fru- 
ftnun oif fi Byranaid or Cone, is the moft 
exa£t . ori any ^ and it may be eailly mea- 
fbred: tht»: Firft of all find cut thc^eighrh^ 
of thewiiole I?yiainid£M^ which you oiaj- 
^ do hy the following proportion, wis. 

As the S:; mi-difference of the Bafes, 
Is to the heighth of the Fruftrum, 
■ ' So is 7 the greater Bafe, 

"Xo the heighth of the whole Pyramids 
UTiicte 



- Which propwhon will hold good in 
Cones as welt as Pjrainids. 

Let AD be the Diameter of the great«f 
Bar*, and BC the Diameter of the lefler 
hak^ from B, and Q let fall the Perpendt- 
cttUra BO and CK^ thentfliall OK be equal 
10 Be, and theStifli 6f AO and KD are 
(be difftrefic* ef dxe-Dzmet^naf the Bjfeft 
AD and BC| and conO^iently AO th* 
Semi difference, and BO the heignth of the 
Frftrunij. and :^ is ~ the fid^ of the grea- 
ttr Bjfe, and.EM la the heighth of the whole 
Pyramid. Then,"' ■ / 

AsAOtFie S?mi-diffiren«ef AerBiaimtet!^ 
Is to BO (he hdghth of ihe FrDflfoxn,'. 
So is AM (4- thi greaP Dijmttir, 
*%o EM the Hfi^hth ef ihti whole Pyramids 

So the heighih of the wboU Pyramid. 
AED,-'(wi!r'Ib8 found to be ?o Foat J [or 
the greater Diameter AD is 24 Incliet,' the 
IdfcfS; the'.difftrence'ifi. the Semi-dif- 
ference 8, therefore UiaU ME lie jo foot ^ 
fof,- ■■■ ---i 

Noi^MVing "found the heighth of the- 
whote Py»lnHl f6 b^;? Pe^,'.rj4irr«by-fiBd' 
the*fcoh(efit of 1hfe^w*«(fe^ffyt9iriid-to'be 4a: 
Foot^.thriv'in ihelefferPyralV^ BCE (here i* 
giren the fi<ie of irs.Bafe BC ~ 8, an J its 
lengrMEib Aictwalfof-'EW 30 — -IMso 
"ait JE^j*, ifo 'I "SiWl thfr CtAii Content oif it 

'-'•■■ book 



99 The T^g Sarv^or*t Gmtl^ 
from 40 tfae coDtent oFthe greater Pyra- 
mid there will remain ;8. %'2 Feet for dl» 
fode folid Content of the Fniftrum ABCD. 
After the fatne manner ii found the fb- 
lidity of the Frufbum of a Coor> And this 
W atfo ufeful ID nKafuiitng of Tapering 
Timber, Round or Square, and for findiog 
the Liquid Capacity of Bccwcr&Cmical, M 
.pyramidal Tunc. 

Of Meafiiwig Jrtifcert Warh 

Becaofe moft, if not all W^orkmen in ca^ 
ing up their Dimenfiooa y make afe of cro& 
Multiplication, I think it wtU not b« am^ 
to give you an Example, (V twaof it, be- 
fbre I enter upon their feve^al nK(hods of 
oieafbriag their Work. 

Note, Feet muUip^'d by Feet produce 
Ftet i Feet by Inches ,piodtu:e Fiet mi /h- 
ebes s and Inches by Incbo^I^odQceJbcin. 
Moi.tvelftiu of hebes^^ 

Feet rncbes^ . 

Therefore (»- awkiply %^%/^^ 
by 4.zSw3' 
PiiA nujlttply the, Feet by the 12 i. o 
Feet and the piodo^iv 12 2112' 1 
JFdet, thearaoltiply crob^w^e o.:^ 

- Feet by Iflshes, ofs..4vby.tf 14^10.4- 
-which; makes s^ilpches or 2 £!«4t and :} hy 
3^ whkh aalix^ 9 iqcbei. ^-S^t Molty^y 



T^e T^ung Surveyor s^ QwJh. Fgi 

dw Inches 6 by ^ and the produQ it iS 
twelfths of an Jficb, or i- 4- lothi ^1 whicb 
produfb fet down and add together^ at.iii 



ihe Operation 








Mrt Eiamila. 


4:2: 
l;8: 
0:1:8 


7a : ot 
S : 0: 
3 !«: 
0. :. 2:11 


37"^^* 

222 : 00 . 
1 : 
12 ■■ 6 
': : S 



55: 11:8 .1 80 : 8 :|i 235:^:* 



Kr^j Glafier* Work^and rab*dand gav^d 

Brtck-work are meafur'd by tluFoot Sqiiarr.. 

Example 

If a Window be 6 Feet 6 Inchei high and 

3 (eet 4 Inchei btoad ) how many Squai* 

Feet of Glazing is there. ^. ai : 8. 



Stcmify^ 



90 The Toun^ Survejfcr's Guide, 

Sicottihf, I^inting, Pariag, Pla&tii^, 
and WainflcDting,are mufur'dby theSguzre 
Yard. 

ExJmpU. 

If a Ceitin?, be i; Feet broad» and 17 
F<;et. 4 lii JbDg,'lKfur;.}naiS7 Yards doth it 
ccotaia^ .A/I 21 !X^rdsi^ 

, - n-V'^ ■ ■ 

321 .0 

25 : 
Tiirdfy^ IVtine, Raftering, and floor* 
iag meafui'd b/ the Squaie, contaiaing zoo 
SqaareFeet 

If a piece of T^Iii^, be 40 feet long 

Bfid 1 3 Feet s lachet' broad : How many 

^uares are (here in it ? 4nf- 5 Sq. 36 Feet. 

.. ■ f 

Square 






The Tou^g Survejfor^s Guilte. g i 
Square Feet. 40"X7"o 



• S20 : 
i6: 



'■'■■'/■'..■' S3i5,:«,. ■ 
Foarth^t ComjpenSiUk-work'ii mea- 
far'd by the Square Kbd,,. containing 272^ 
Square Feet ; But i£-lll£.JB''jIl be not one 
Brick and half thick , , it miifl be reducf d 
(0 that Standard, by ^liis General Rulfv 
Multiply the Sipei-ficial Content of the 
Wall by the thieke«fft~-thertof in half 
Briciit i divide that pnodD^ by 3^ and il 
gives iht true Qpantity* '' 

If a Brick Wall that ia^U Pppt-thic^ 
be 40. F^et loofe^, ind 9 Feet 11 tnchea 
higb. from .the roiindatibn, it ■wiUeimf 
tain xRod" i.Qu.jf^/Feet, ." 



■ I 124:5 1 



Exanu, 



S*j Tbfi Toung Sunirfer*t Guide,. 

If a Bricic Walt i Bricks tbidc be f 
F«t 6^ jiKhei in length, and 14 Feet 9 
Indin in breadth ). the true ctHitent after it 
ii reduced to the Standard, inz, i, Brid^ 
» ) Rod, 2 QusftM-«i 40 Feet. 

700 : o 
37:6 ■ 
7 - 4 

_ . 744 : »o 
Kumb, 4- Bricfci 4:0" . ; 

i)29-j9 : 4 (99 J 

Whidi dm^ by "o, 272T, giv** 
3. Rods 17^. Feet : Which ia the tnie 
Content of the Wall. , , , 

A^. B. The Bricklayers have a naiticu- 
larwayof mcafuring Chimneys : Which ir 
by multiplying^ the Girt of the Chimne^i 
ty the heighth thereof, from the Foundati- 
on to the Hearth of the next Chimney » 
jHld the thjckneA of the Jams ii taken for 
its thicknefs % which method they follotr, 
till they come to the Shafts. 

/^nd Ihofe thejf fiiit for the length of a 
Wall, the heighth ctf which is the heighth of 
the Shaitt and the thicknefe always two 
Btickav ^«"Vfc' 



The Towig Si&rveyffr*s Guide, ^| 

' BxampU. 

■ If a ChinlPey be 24 Feet 3 Inches abwit, 
its Heighrh 9 Feet f Inches, and the thick- 
nefs of the Jams one Brick and half, what 
will he its Content? Jfif- o Rod 3 
■Qu. 24 Feet. 






SI6 





10 





a 


^ 





I 



228 : 4. J«f. in Feet* 

7S«s, ThiM they meafure theChimneyi 
of every Floor till they come to tiw 
Shafts. 

If the Girt, of theOiimney Shafts be 
20 Feet aQd the heighth 1 2 Feet 3 Inches, 
hour much is their Content ? Jup o RoA 
3 Q."' 4^ Feet. 

2o"^i^o 

3+0 : o 

S •• o 

fbe 



e4 Ti>^ Toang Saneyor's QctiJe, 

The meaforiDg Book ought to be divid- 
ed into three Colanmt ( <u tbt Exntple 
Jl>£wi ) in the firA, the Kames of the Dt- 
roenfioBt are f«t dowD, in the ftcoDd, the 
pimeDfiont themfelvcs, and ia the USr thf 
produd of thofe Dimenlioni. 

After you have takin, and fet down the 
Dimeufioni; Your next work* i< to maltipjy 
tbem upon a wiAe Paper, and fet down 
their produ£h over agjinJt tbem in the 
fecond ColuoiD : At-ysaotyiW in tbe 
Gample. 



JKnut 






^The TaiMg Svrvej&i's Guide. f^ 
N.imcseftheDm. D'mmt TidrDrtJttBs. 



FheGiriof ihe> 
4n<I«ioD:WalJ ( 
King 4 limc*^ 
Thicknefs. , ^ 



FheGiriof ihe;j 
F0w<I«ioD:' 
abating 

its Tiiic . 

Thf Heighrt. 

Chimneys Girti 
Hdghih twice. 

Windows deduce 
three limes. 

Door dedai^. ■ 

Girt upper Wall 
Heighth. 

Chimneys twicr. 

..'^JB4tiws4edtlc., 
: 7 liaie*. 

Chimney Shafts 
4viccb ■ 



F. In. 



3f>tO 
I2;o 



7:0 



115:4 



2^:0 
9:6 



i7-,o 

i:6 



12:0 
410 



= i384,Feet. 

liB 
= 624, Feet. 

tiB. 

= 73 F. S Id. 

t iB. 
= 28 Feef. 

li B. 
=149^4.111. 

iB. 
= 494 Feet. 

it B.I ' . 

='i7lF.«In. 

.2. B; 

?= 96 Feet. 



Kow 



9* 

Nov to cad up 
llwir Dimeofions: 
make 4 CtJamns, 

8sinthrMargin,in 
thefirftsf Which 
patall theprodu£t 
•Fone Bride and 
half ThicJcnefr ' 
that are not De-. 
dufliom, ir there 
be any of 3 Bricks 
thick put it dovn 
twice, efc. thrn 
pat downaU «• 
cept ^edu£iioot, 
that are oneBrick 
thick^iftwOftwice 
wdiffoBlyhal^ 
as in tfaeEzaoi- 





tBr. 
F.H. 

3907-4 
a7j;2 


1 Br. imr. i.m 
F. F. Id. 
4«:o „,« 

9A0 I7i:tf-| 

(S8rf:o 373:3 


J254'"' 
4S7H 


R. Q. F. 
= 13 am' 




. -■; ,_ 1 


3> 378(457 
•a* 





iI7!3!««.o)(i3. 
»73 



Then aii up the £rft Colamn, from the 
'Sbqi of which, l{ibllra£l the Sum of' the 
•Column of Bfick M(thalf DiduaionH al- 
fofromlhe Sum of the fecond Column, 
fubfiraa the Sum of the one Bride DftJuffi- 
ons, pf tbm It mif^i^lhcu tedxKe the Re. 
mainder to the thicknefi of a Brick and 
ilali^ and add • that rcfult to the Remainder 
of the firfi Column, which gives the Con- 
«nt of the Brick work in Feet, and the 



B' 



Tl&f Toting Surveyor's Guide. ay 
Rods are found by dividing it by 272 i 
As plainly appears in the Operation. 



The Art of Surveying and Mea- 
furing of Land. 

Fhjl of the Chain, 

Ecaafe Mr Gmter'f Chain is nwft in xtte 
) among Surveyors for meafuring of 
Lines, I ihall diiefly infift on ihat Mea- 
fure, it feeing the beft in tife for Lands. 

This Chain contains in Length 4 Pole or 
66 F«t,, and is divided into looL'nks, 
each Link is therefore iiiLength vl^^inchej: 
If you wouW turn any Number of Chains 
into Feet, you muft multiply them by 66. 
as !oo Chains multiplied by 66, makes 
6600 Feet ; but if you have Link's to your 
Chains to be turned into Feet and parrs oJF 
Feet; you muft fet dbwn the Chains and 
Links, as if they were one whole Number, 
aiid after having miikiplyed that Number 
by 66, cut from the produia the two laft 
Figores to the Right Hand, which will be 
the Hundredth Parts of a Foot, and thofe 
on the Lefthand the Feet required. 



Example, 



jSj The Tom^ Surveyor's GuiJg* 

■ Example. ^ .. /.j .;■ 

Let it be required to know how many 

Feet there are in 15 Chains 27 Linkf. 

I fet down tlius the Multiplicand 15,25 

Th» Numbej of Feet ia i Chaiq, 64 

Multi^tyer.' h— — 1^ 

.. ■■■■ : .- : ■' 9150 

91 yo 



Prodod in FmC. 1006J50 > 

. ■ Tht Produft is roo6 ff^: Thii. it fo 
fjlain, it needs do other Example. 
. , Rut now on the <»tber haod, if ope tfaou-; 
fdnd ttkd. fix Fee^ st)il an half was ^veii yout 
fb reduce inioCf^ifie and Lifiks) 70U iinpA 
divide ioo<S'yo by <S6, the Q.uotieat ^iril} 
tie 15, 2J, */|l. If GhaioH 35 Ijnkp. 

[b hk« inannuf, if. it had beeA aiJud,* 
IjGW tn^ny PerchM b)^ been canrainedrio_ 
1.5 ehal^s £5 Lij^s, iyottiroaft ^ida-i^, 
2-\ by 25, *h^ Linlfb in me Parch and th«. 
Quotient Aofwers the Qtieflian. , 
^j.Vi5,25(6i. Aflfwer in Per^tec 
.'i?o ■■ . '. / .. 

'. '■"^5 :'/ "■'" ; ■■■■ '■' '-.:■ '• ■: 






The Taung Surwyor^s GuiJe. 99 
Admit I would know Kow many .Chains 
are .contained in joo Feet. 

. Operation. 



38 Aftf. 7 Oiaios 57 Lia. ^y- 




tg Meaftire* . 

ftjches 

Feet. '' 



66q\ 22o[ ■ 
28o!l76c1 j: 



;2o I g^o 220I 4° Furl. i ■ 
S,iiio ;28o|l76c1 i 2o - .8 IMilk 



P 2 . '' A JaUs 

4 



-leo 

S 3. 



The ToUng Surveyor's Guide, 






S 







1 


> 


-57 


3- 


§ § 

O ° 


^ 


IJ> 




1 




1^ 

1^ 




' 








1 






? 


1 

1 


i 


I 





1. 



W\ 






The Toung Simjeyor's GitiJe. lor 
The cooimon Meafure for Land is (he 
Acre, Vtiich by Scatute is appointed to 
contain i6o Square Perches^ and it matters- 
not in what form the Acre lyes in , (o i« 
contains ]uft i6o Square Perches : As a P^- 
randogram lo Perches one way, and i6 
another contains an Acre-j To dees 8 one 
way, and 2oaiiother, and4.one way and 40 
the other. If then, having one fide given in . 
Perchsyou would knownow far you mufl go 
on the Perpendicular tocut off an Acre, you 
muft divide 160 (the Number of Squ-ire _P.r- 
cbei in at Acre) by the given fide, the Quo- 
tient is your Dfirc. As for Example, tlie 
given fide 20 Pe;che8. ■ Divide 160 By 2o 
the Quotient is 8, by'this I know that 20 
Perches one way, and 8 another,including a 
Right-Angle will be the twofidesof an-Acrer 
the otlier two fides muft be parallel to theO. 
And here 1 thinit: it convenient, to infert 
this necfffiry TiIjI"", fhewing the L-ngih 
and Breadth of an Acre in Parches, Feet . 
and partS:of a Foot .• But if y oar given fide 
had been in any other fort of Meafure^ as 
for inftance in Yards yon muB then have 
feen how many Square Yards had been in 
an Acre, and that Sum you muft have divi- 
ded by the Number of your given Yards, 
the Quotient would hare, infwered the 
QueflioD. ' 

F 3 Breadth- 



lo^ The Tcufig Snrviyor's Guide^ 

2 Length of g Length of 
& aoAcre. Si an Acre. 



















!? 


•9 






'^ •□ 








s 

3- 


?? 
? 




1 


S 
























? 








«• 






lo 


Ill 


.0 




28 


5 II i 


















II 


14 


9 




29 


7 01 




















la 


•3 


5t 




?o 


5 


f i 




















>3 


1_2 


5tt 




3] 


'I 


2 Y 




'4 


II 


-i 




i? 


_5 







!^ 


10 


II 




33 


4 


-il. 




i6 


10 










_i 


ILi 




17 
18 


9 
8 


14,1- 




3! 

36 


;4 
4 


9 t! 

7-7 


















i^ 


8 


_#j- 




37 


_i: 


5 t 




20 


8 







IS 


4 


JJ 




!i 


_7 


lOrf 




.11 


j4 


Jlj: 




22 


.7 


4-7 




40 


4 


"6 




















■H 


6 


1;^ 




£r 


J 


i+ij 




2 + 


6 


11 




42 


3 


13 t 




2'; 


6 


j3 




43 


J 


iiU 


- 


26 


J 


27t 




44 


3 


■*o t 




27 


5 


i!t 




4S 


1 ?v 


"- 


^ 












■Ea' 





The Toung Surveyor's Guide* loj 

Example^ 

If 24 Yarfs be g/vea for (he Breadth^ 
"ho^ many Yards fhatl these be id length - 
of the Acres. 

, fi^fi^ I find tbat an A^re contains 4840 
Square Yards, which I divide by 24, rhe 
Quolient is 201 tr for ihe Lengih of the 
Acre" And thus knowing wilt how to fake 
theLengthandBreadthof an, Acre, you may 
.al(b by the fame way know how to lay 
down any Numbef of Acres togelher. 

Reducing of one fort of Square mearure 
to another, is done as before ta^ight in Long 
meafure by Mnlti plication and Dl'vifion. 
'And becaufe Mr Gmtert Chain is chiefly 
ufed by Siirveyotg, I ' fliall only inflanre in 
that, and fliew you how to turn any Num- 
ber of Chains and L'nks into Acres, Rods 
and Perches : A'ute, that a Rod is the (onrih ' 
,'pirt ef an Acre, 

■ A-n3 fifft mark well ihat 10 Square 
Chains make an Acre, that is, to faj', one 
Chain is Breadth and lo in L-jigth, or 
2 in Breadih and jr iii'Length, is tlie' 
Acre i as you may fee by this fmall 
Table. . 






1 04 





n 




f TS 




3- 




3 


ET 




w 


El 


a 


I 






2 

3* 


2 


» 


?3 





3 






■*i 










4 








5 
6 


31 

3 


66 


? 


7 


> 

5 


23 




9 




11 



71&£ TTwnj Surveyor's Cuitie* 

And thus welT weigh- 
ing that 10 Chaini 
make one Acre, if any 
Number of Chains begi- 
' ven youto turn into Ac. 
you maft divide them 
by ici, and the Quo- 
tienf will be the Nim- 
ber of Acrts contained 
ID (o many Chains. 

But ibis Divifion, is 
abbreyb^ed hy on- 
ly caiting off the laft 
Figure, as ir 1590 Chains were given to 
iiitointo Acres, b/ culling off the laft Fi- 
gure i^^.'o, there is left 159 Acres, which 
is alone as if you had divided lypo by la 
But if Chains and Links be given you to- 
gether to turninto Acres, Roots and Perches, 
firft from the given Sum cut off ; Figures, 
which is 2 Figures for the Links, and one 
for the Chains, what's left (hall be Acres. 
And to know how many Roods and P.-rches 
are contained in the Figures cut off, Multi* 
ply them by 4 from the produfl, cutting " 
off the 3 lad Figures, you will have the 
Roods ; And then to know the terchef, 
multiply the Figurees cut off from the Roods 
by 40, from which product cutting off a- 
gain 3 Figures, you have the Perchis, and 
the Figures cut off are a Thoufabd parts of 
a Peidi. 



Tie Teung Surveyor's Guide* 105 

Example. 

1599 Square Chains, and yj Link*, 
bow tmoy Acres, Roods and Perches. 
Acres 1591 555 

_t '■'■'■ 
An/. 1 59 Ac. 3-Roods. Roods i\% 20. 
32 P<rches. 800 40 

1 000 Pdfches ?2l8o3- 
On the cooirary, if to any Humbtri ot 
■ Acres given, you add a Cypher, tliey wifl 
be turned into. Chains, thus s>9 Acres are 
S90_ Chains, .100 Acres looo Chains, £?'r. 
the fame as if you bad multjplitd the Acres 
by 10. And if you woultt-jarn Square 
Chains into fguare Links, add four Cyphers 
to (he 'end of the Chains , ff> ^ill ' $90 
Chains bs 9900000 Links, looo Chains 
1 0000000 Lrnlcs, all one as.it you had- 
niultiplyed 990 by loooo, the Number of 
Square Liiiks contained in one Chain. 

And now , whereas in Cafting up the 
" Content of a piece of Land mea(ured by 
MtGmtcr^s Chain, viz. Muliiplyiog Chaios 
and Links by Chains and Links, the pro- 
iuH will be Square Links ^ you muft there- 
fore from thai produ£t^ cut o^ ; Fi£urei 
to find the JVfres j which is the Tarns as if 
Toudividtdthe produ^by looooo.iheKum- 

Fs ^ to 



I off The Young Sarveyor'i Guide, 
ber of Square Links contained in one Asre, 
tlien mtilriply the 5 Fi^ores cul off by 4 -, 
and from (hat product cutting off 5 Fi- 
gucffi you vriW fave the Roods. -L'*ftl}\ . 
Multiply by 40. and lake away as betoce 
% Figurei, the teA ire Perchet. 

A4mit a Parallelogram,' or long Sftiare, 
to be one way ; Chaini 57 Links, and ibe 
sother way 4. Chains 35 Links: l demand 
^ ihft content in Acres, Roods and Percfcw. 

Mnltiplicand. ■ 1 ^55 

Muhiplicator. 4^;. 



'A<nf. ya Acres. ^ . 2775 

J. Rood. C 2220 ■ 



3fi Perchflfc \ ;Acr<s-2|4i42; 
■ ■ ' ,4 

And T-rr P^f's of ■ a Perch. 

PeKhes 2<5! 28 000, 



QflnfirumenisandtheirUfe. 

THjre are feveiral forts of'ChaiftS, as Mr.. 
Rathhotnt of 2 Perch long; Other jif one 
Peich long'i Tome hays had them 100 Fe«t in, 
Length :. 



■TBiT^ung^ Surveyor's Guide, 107 
l^eogth : Bdt that wjiich is inoft in ufe a- 
laorg^ SorveyorX ^s being indeed the bell, 
ie Vit Gimtett, which is 4pples long, co).~ 
UtniiJg jop Links, each Link b?ing 7i— J- 
■fcDches : The defaiptionof which Chain yon' 
have had already : Id this place I ^all give 
von fixn^ fevr dife^tioos for the ufe-of it io 
Me^urUg LiRt4? Ts^' ^^■'c that Uwy w]ikh> 
^ty ^( Ch«io deviate not ftoma firejght 
LisCf which yew may do by flaoding M 
your InSrameiir, and looking through the 
lights. U you fee them between you. and: 
the Mark obferved, they ^e in a ftreigh* 
X^ioe, otherwire Dot. Bnt wiljiout.aU this, 
irooblfl,. they ro»y carry. (|ie Cbain friie 
enough, if he that follows tlie Chsio, al- 
ways caufes him that goes before him to be 
in z dve£t Line betveen himfelf and rhe 
place they are going tOj fo as that Jhe" fore 
,. Man may always cover the Mark from. 
him fhatgoes behind. . if they (werve frotn- 
Ihe Line^^they will make it loijger than 
really it fs j a flreight Line being (heneareft - 
diflaflcethat can be feetween any 2 places.. 

Bi fqre that t he j which carry ihe Chaih 
miftake not over or under in tbtir A^-connf,, 
iat i1 they (hould, the the Error would lid 
very cnnfiderable^ 

But the ufual way fo prevent fuch jmt- . 

takes is, to be providwl with KiTmall ftitk* 

3(bar£*d at one tfndto fiick in the Gfound^ 

,- an* 

„ . Goo<;k- -^ 



ipB The Toung Surveyor's Guide, 
and let him that goe§ before take all into 
his hand at fetting out, and at the end erf* 
tvery Chain ftkkdown onej which let him 
that follott's take up, when the lo flicks are 
dpne,"befu« they have gone lo <- haio«i 
then if the Line be longer, let them change 
the flicks, and proceed as before , keepirg 
ID Memory how often they change. They 
tMy either change at the endof loChaiur^ 
iheii the hindermofl Man gives theforemoft 
all his fiidcs, or which is Utfer at the end 
of It Chaini, and then the lafl: Man. muft 

five ihe &ft but 9 flicks, keeping one to 
imfelf. At every change count ihe ftickg, 
for fear yon have dropt one, which fome- - 
-times happens. 

Of Injiruments for- taking of an Angh 
in the Field, 

THERE are but two material things 
to be done in the Field, the one is to 
Meafure the Unes, and the other is to mea- , 
fure Ihe Quantity of an Angle included by 
ihefe Linfs j and the Infiiuments of the grea* 
teft efteem, are the plain Table for finall 
Inclofi'res, the Semi-Circle for Qiampaign 
Grounds, (he Circumference or the Theo- 
dolite, i^c. To defcribe tbefe lo you, their 
parfB, how to put them together, take 
4hem afuoder, i^c . is like teadbirg the Art 
- - of 



. TheTdung Survey&r*s Guide. 109 
of Fenring fay Booki one H:ur8 nfe of 
Ihem, or btit looking on them io the Inftru- 

ment-mitkiTs S^op-, will ' better defcribe 
the 111 to you ihan tbeReadiDf;oneHund[cd 
Sheets of Paper concerning them. 

To take the ^latitity of an Angje. 

Fig. 84 Let AB and AQ be 2 He%» 
of a Fi^ld, to'£nd the qi^aoticy of the- 
Argle A hy the plain Table. 

Phce the Table as oigh to (he Angle A at 

?ou can, the North end of the Keedlc 
anging dired]y over the Flower de Jjict^ 
then mikt: a Mark uptm the Sheet of Pa- 
per at arty conftant place for the Angle A, 
and lay the edge of the Index to the Mark, 
farnirg it abbu% till through the fights you 
efpy b, then ^raw the L'ne AB by the 
edge of the Indei. Dd the Ume for the ' 
■Line AC, fceepng the Index ftiU upon the 
filfl Mari:, tlien will you have upon yoat 
Table an Angle equal to the Angle in (he 
Field. 

To tahthe gomthycf the fane Jiggle Bj tU 
Semi-C'tcle, 

Place your Sfmi-Cifcle in the Angle A, 

~a< near the very Angle as pcjfibly you tuq^ 

and Canfe Marks to be fet op nigh B aod^'C, 

fo £ar oS the Hedges, as your InfiruiBeiit 

at 



at A fiands, ih«D rum tbe Inflrament a- 
bbtrt fill throDgh the- find fightt ypo fee 
the Mark at B, there Screw it (aft j neK 
tiini the moveable Index till ihrongh the 
fights ther«(^ }>q9 («e the M'tk at C, and 
fee what deg. upon the Limb are cut by 
the Index V which let he 47, fo much is the 
A'glc BAG. 

.' Hij* totaki iyefjiht. ^fhvCiretimferetitor.: 

^X9 your Inftrument as befoce,- with 
riie Ftovwr de Luce iosratdt^you , then 
direft your Sight! to the Mark at E, and 
IH What degre«i aM:iheit cat by tfle Soirifa 
end of the Needle, irfach let be ^^y dothe 
Xami'to the Mark at- C; aad letthe Needi« 
tfiere cut' 100, Sobftrad the Itffa out ot iht 
greater, and ^e Remainder is 4;, the Afigt* 
rt-quired. IF the Remainder had heen more 
then 180 flegrees, you niuft,ihen haye ftil- 
Hraaefl it out of 360, the lafi: Remainder 
^uld l^e - bem the Angle defined. 

£bw hy the Semi-Cirde to tah the ^anthyof 
'an AngU in the 'FisU hy the A«dJe, 

Screw faft the Inflrumetit, the North-end 
i<(ff the Keedli- hanging direSly ovef the 
'Slower de L«ce in the ' Chord , turn the- 
ilndei abouf, till- through th 3 "Sights you 
f£7 the Mark at B^ iind aote what dfgree^. 
tha: . 



The Tmrng Smtepr*s Gidcte, i n- 
the Iniex curs, which' let be 40 ; move a- 
gain the Index to the Maik at-C, and mm 
thed^M cur, viz. 55, fobflrat^ tbe lefs 
from the greater. Remains 15, the QuaO-^ 
tit/ of the Argle, 

Note, If you mrn the Flower de Luce to- 
ward! the Marks, you mufl look at the 
l^orih-end of the Needle iot ydat deg^es. 
^od the Eaft and Wffi pokftB are matkecl 
contrary, viz. £aft with a W, and WeS 
with an £, beciufe when you turn the In- 
Arument to the Eaflvard, the end of the- 
Needle will hang over the Wefl-fide, fcJ'e, 

If by this way oi Jiiviiiaa of the Chord, 
you itovld takp the afprefaid Angle, direft 
tint la^tument (fo ^^ Pknrer m Lme from 
fou,) till through the Sights you' efpy the 
Mark "at B ; then -fte w h a t d eg rees -are cut 
by the North' end o£ the Nedle,.. which 
let be N.£,44; next direct the Inftriiment 
to Q and (Tie Nirth-end qf thf Needle will 
cut N- E. 89. Subftrad the one from tlii 
'other, and there will Remain ^^j. for tb^- 
Angle. ■.■■'', 

'GftheVieU S00I ' " 

Too muft always have iit readinefi in, 
jhe Pield, a little Book, in whi^h fairly, to 
ipfertyour Atales'and Lines s wliitjh Btiok 
you may divine by l.inea into Crfuinns , 
K YdU Ihall ibink, couvenieftt in your 
Ptaajca 



113 Hie Teuag Surveyor' t Guide, 
Vti&xce^ having always a large Columa 
to the Right-hand, fo pat down remarkable 
thing! you meet with, as Brooks, Mills, 

Example. 

If yoo had taken the Angle A, and found 
it To contain 4? Degrees -, and ineafured (he 
Line AB, and found it to.be 12 Chains 
;; Links, fet it down in your Field Book 
ihcs. 



A deg.|MiD.|Gl>.|Lia 
45 1 00 1 12 1 2! 




1 1 . 



Z.(tjilj, You may chufe whether yon vriH, 
have anjr Lines or not, if you can write 
flreight, and put the Figures diredly ont 
under another ^ for this I leave to your own 
fancy i for I believe there arc not two Suf • 
freyon in Enghndj that have exadiy the 
ikme Method for their Field Notes- 

Oftbs Scale, 

Therfr are feveral forts of Scales, fame 
larg", fome fmall, according as Men haw 
occafion to ufe them, ior the laying down 
C lalna and hinks } ^fo you have «pun 



The TmngSurviyorsGutd*. 113 

the fame Scale Lines of Chorda, for laying 
down and Meafuring of Anglts. 1 :anno 
belfer-eiplain the Scale to you, than by 
fliewing the Figure of fuch a Decimal Scale 
as I think mo^ ufeful, and are commoalj 
.fold in Shopa. 

Of the PrttraSor. 

The Protraftor is an Inftrument with 
which, with more eafe and eiadlntCs you 
may lay down an Angle of any Number 
of Degrees, tlian you can by the Line of 
Chorda : And when ynu have Surveyed by 
(he Needle, by pacirg the Diameter of the 
Protrador upon a Meridian Line made up- 
on your Paper, you readily with a Needle 
upon the Arch of your Protraaor, 'ptjcfc 
' oiTthe true Situation of any Line from the 
Meridian, without fcratching the Paper, aa 
you mud do in the ufe of the Line of 
Chords. It i> made almoft like, and gra- 
duated altogher like the Brafs Limb of a 
Semi-Ciicle, performing the fame upon 
Paper ,- m your Infbument did in the 
Field. , ., 

Haw to lay iuvn an. AKgU with tb« fVc- 
traSoT. 

fig. 8y. If it were required by the Pro- 
traaor to lay down an Angle of 36 deg. 
Draw 



it4 TZ>^ Tffung Surv^or*s (juiSe, 

Draw ibe Line AB,_then take the Protraflor 
and putting the Needle through the Cetitei- 
p()int thereof, place the Nwdle in A, fo 
that the Center of the Ptoiratlor m?i^ ly^ 
^'uft upon the Liwe « A, move the Frc- 
traflor about till you find the Diameter 
thererf lye upon ihe Line AB; then at ?o 
degrefs upon 1(15 Arch, witli_your Proirail- 
ir.g Needle make a Maik upon the Paper, 
as at C, draw the Line CA, which (hall 
make .an Angle of qo degteej , viz^ 

BAG.- ; 

tiov to Jay iotnt the 'Angle "by tbs Line of 
Cbordi. 

Fig, 8(S.If it wrTc Tequrredto mafre aft 
Af^glethatfliDuldcontain 4.5 tjfgees. Draw 
a Line ar plearure, as AB j thtn fitting one 
Foot, of j'our Compaflis at' the beginning, 
of the Line of Chords, fee that the other fall 
juft upon 63 D.greesi with that eitent fet 

Diie Foot in A, and defcrite the Arch CDj 
then .taftfi from your Li^e of Chords 47 
degiTK, and fetting one F'^bPi'n D, make a 
Mark upon the Arch at C , (hroigh R-hich 
draw the Line AE i fo (hall the Angle EAB 

■ be45degreej. If bjiheL'he of Chords you 
would ereil a JPerpendirular Line, it is no 
more but to jnike an Angle that ft)all coi> 
'tain 96]t)fgrefS. ^ ■ 

;■■ ;,-■ "•■ ■ ■ ■ ■ - .- ■ •The. 



The Tirnng Surveyor's GuiJe. x 1 5 

The rea&iO why I bid you .take 60 froiil 
At hiao nf Chcads to. make yaw Arcli by, 
is becaufe 60 istheSaJni-diatnetri of h Citcit 
vioU Gircanifereiice is ^6o- 

• How to ca(l up the Content of dfigufe, 
the' Lines being given in Chains and 
Links, 

HAving defciibed ihefe plain tnftrunwnts* 
and in fome me^fuie {hewed the tfCf 
of them, I intend to (hew him, i; How 
he ought to make his Computations 1 2. The 
Groands or Principles that will jufiify him 
in fodoing. -- 

For thfi ^irfl takt thefe -Ek/mj. .. 

-I. Pat ■down your Length .and 3readtFi 

- of Squares and Oblongs , and your Bi(e 

and t Perpendicular of Triargles "direftly 

-under one another, eipreilid by Cliains and 

Links, with a prick betwixt them. 

2. If the odd LiuJu. W££e under 10, put 
3 Cypher before the Figure^ fiprefling them 
as Chains and Links ^ arid if there be no 
odd Links,' but alI«v«H Chain?, put two 
Cyphers after the prick,. 
* ?. Maltiply Length by Breadth, and 
,Bafe by i- pBrpindTnriar, -according to the 
Rules forfioding the Gentent-of Figures.. 

4^' 



xi6 The Toung Survejfor*s Guide. 

4, From that ptodu^ cut off ; Figurei 
reckoned from the Right-hand badcwards . 
with a dafli of your Pen, fo flial) thx^ on 
(be X-efthand be Acrep. 

^. If thofe on the Right-hand ureie not 
all ; Cyphers, multiply them by 4, and 
cutting 0^; toirards the Right-hand zgiin, 
the reu on the Left-hand will be Roods or 
Quarter*, 

6. - If amongfi thefe <; Figures towards 
(he Right-hand that were cut or at the fecond 
Mulriplication, there be any Figures befides 
Cyphers, multiply all the 5 by -jo, and cut- 
JBg 5 again w'th 3 dafli of ym:t Pen, thofe 
00 the L;ft-hand are Square Parches. 

ExampU I. 

What is th« Content of a Square, whofe 
fidei are every one of them ^ ;o Lio^t- 
Length 4, jo 
Breadth 4. %o 

22500. / 

r£oo 



210 2500 
4 



1 oooo . 

40 A'if. t Acres and 4 
- — '- "' Perch, as appears. 
4I00000 

Exatpfle 



The Toung Surveyor's Guide, 117 

Exa$apU -II. 

I-ct-a long Square, whofe Length is 14 
Chains, and B t-adth 6 Chains and 5 Links 
what is the Content > , 

Length, 1 4. 00 - 

Breadth, 6.0$ 

70C0 
, 84000 



8I47000 



'' ■ ' "-J^/ 8 Ac. I Rood, 

. ;il47Coo 35PeKh?8,.asthe 

40 work makei evident. 

35{2ooo(i. 
Example: HI.. 

Then h -a Triangle, whofe Bafe is 3 
Ghains, and f the Perpendicular is 4y Lin. 
what is the Contenr. 



. The, 






Ji3 Th''- Tomg Survtjfor's Gutdtp- 
The Bafe 3.00 
Half PerpeP' o. 45 



IS 00 

ISOO 


A. K f 

Atf. 0-0— 21 


1 3 50.0 
♦ 

540 oe- - 

40 




, aii^coo© 





1 1 fliiU Dour demenAfate this vny of 
caftii^.Bp a pifc«of.i.^nd-by the follow- 
ing. SS^. 

1. Itis evident, tti«tm<his way of Mul- 
tiplication, the ptodoStis -Square Links -, 
for every Chain being a Hundred Linki, 
it is all one to .pulrifljy -4- Jo, by 4.50 or 
450 without the Pricks, for they fignity no-, 
tbing at ill in- OpmlioSi ' Tfac pcodu^ 
rh^4tor« of the fcft Eaunple wn -icAi 
500 Links/ . 

2. Every Chain being 4^erche« long, 
it follows, that ; Chains in Length and 2 
Chains in Breadih,- make an Acre, or 160 
Square Perches. 

3. FrorolKnceiit plainly follows farther, 
that therC^ are eiaftiv looooo Square Lin. 
in an AcEe^ for 5 Chains multiplied by 2, , 

it 



• 7^_Toim£Surve^ar*s Guide, ^igt 
ii the fame with ;oo Links ty 200, which 
mafeea iQoeoQ; , Then according to theOW 
" phia 'Kiile'irt- Aritfimeticlki 'ivhsn the Di- 
Wftr cDnfiRs of 1 and Cy^hets; t^to^ioo^ 
iooo, looooo, f c.) cut off from the Rtghn 
Hand fo many Figures of the Dividend aa 
'rite DirtGkr'fc^X^fpfafrs, 'atd countiiig 
them for the irsraains, i (o ihati tfacirtft ba. 
tJjsMtffde le *he Qliotitnt. It- i*. plain- 
then tiiat i.^y.'}c6 rqgaf& Links raxkes i- 
Jictty ilod^75o6 fqgjir^ ^iolu over. 

So I have iDad« it dear, ks farstctmcerns 
Acrrst that the: Rules fprOHnpuutiDn arv' 
good.. N(»w inr IRmidf aind'Pecchia,. it it 
plairefrem rimtkneiifOi' Euii. in D.ciaial. 
Acithinentcfej Multiply tbe giv«n Decimal- 
by tbe Ntimter of parts in the next inferioBr ' 
dfoofniiialim, dsat-are cqu^Jo an Integer. 
in diA'fame deaammation with the giuea 
pBsimBJ^Bnd.ffe how. many .pjaccs arsiu the 
*4^8di]tI;,Jinire-tban<*eraJB!liifc/giSien;Deci-r'' 
mal 5 and cut fo many off from the X'ifC-- 
fi»nd, jtAA'jfUafetFipansjB cmcff,- are the 
vjiIae'«t.(WK)idI>cin3Bl.! So that ,tii:i way ' 
of caflifigupthe.Comeat of a (liece^f L^ 
is tnM'^ *i'.. '. ■'»■;' ■■' •■■ i . ■ .'' ' ' ' 






120 The Toung Survej'or*r Guide. 

HoTo to meafure a piece, of Land, and 
to PratraS it^ and to give up the 
Content* t 

AL L Clofes, or P<irce1s of Land, are 
either fuch as need not to be ptotted 
for finding out their Content-, but the Chain 
alone dorS'the worlct or fuch as cannot be 
meafured withont plotting or Protradion^ 
of the firfl fort are the Squares and long 
Sqaares* and thefe, I fay, need no plotting, ' , 
for )'oa need only to niultiply the Chains 
and Links oflhe Length,' by^the Chains and 
Linkaof the Breadth, fo proceed as in the 
lift Examples: Bilt all others, whether Tri* 
angles or Triangulate, are to be protracted. 
I ihall give Examples therefore in the- 9' 
forts of Figures, Triangular, Quadrangular, 
and Mutangular. Eut let me adviie the 
Young Praditioner to remember tbef^' 
things. 

I. To begin at fomt notable Angle of 
the Field, where there is fome Gate, Style, 
&e^ Or if there be none, to dig up 3 
Clod, or at leafi to obferve what Quarter 
of the Heavens it pointerh toward, and on 
your Pdper mark it with fome Letter. 
- 2. To go Parallel to the fide of the Field, 
accuftoming your felf to go' either with 
jour Left-hand towards ihe Hedges, or , 
Contra 



The Toung &trveyor's Guiiie' 121 
contra wjih your Righc-band towards tliein ; 
arid wlien yea go -con-triir)' to jo^ir ufual 
Cuftomirioie it on j'our Pjper by (brae 
initk known to" youi f*I^ 

3. To take heeJ, left yoQ contound 
your I'elf by raking Lines off of Teveral 
Scales, or mearudng Perpendiculars upon ■ 
itrrong ones^ for every Line of the fame 
F^ure maft be made by the fame Scale, 
and (he P.-rpeadiailarstneaftired by it. 
- 4. To make life of a large Scale in fmall 
CldTes, and of & fmaller when you meafure ^ 
great onei 

y. To fet on your Chaini and Linki at 
twice, when say Line is too long for youc 
Scale. 

Thefe things lielog pfeiTiifed, 1 proceed 
thus : 

Fig. 87. Suppofe ABC tobe a Clofe, be- 
ginning at ihe Eaflein Angle A, and going 
with my Right-hand towards the Hedgp, 
I find the iid*a to be 4. 07, 2. 29, 3.4;- 

I firft, with my CompalTes, take off (rem . 
my Scale 4 Chains and 7 Links, and f?rtirg 
it from A to B.'draw that Line for thxBate, 
becaufeitis tHelongeftof the three; Then 
I take 2. 29 off the fame Scale, and p it one 
Foot of the Compafles in B, \ defciibe th« 
Arch OK. N-'ir taking with my Compaffea 
upon the fame Scale, the eitent of 3.4;: 
I place one Foot in Hie poiit A, and Rjtfi 
the ether make the- Arch PCi, interfeaing 
G A 



f; 



J as The Totnig Surveyor's Guide* 
the other in tlie point C ; and drawing the 
L nes AC and CB, the Triangle ABC it the 
Plot of the Field meafured^ 
K zt X muft find the Length of the Per- 
endicular, which is done by fttting one. 
'oot of the CompafTes in C, and eirending 
the other to the Bife AB, fo as it touch and 
pafs not over if; then the Leng-h of the 
Petpcndicular is between the points of *he 
CompalTes, and it being applied to the 
Scale that the Triangle was made by, zi 
appears to he" f Chain 42 Links i ivith the 
4. whereof I multiply the Bafe AB, 4. C7, 
and proceeding according to the Rule before 
delivered, the Content appears to be o 
Acres, i Jlood» 6 Perches, as is evident. 

Hie Bafe 4. 07 

f Perpend. 0-71 

407 , 

2^49 

28 8 97 

.^ 4 ■ 

HI 5y8 8 



6\2Z t2o 

The Content of this piece of Lind may 

be very leadil/ fouod without plotting 

ir. 



The Toung Surveyor's Guide. 125 
' if, thus : Firft, Meafure the Bafe. Line A&, 
then by the help of your Crnfs Staff, find 
where ihe Perpendicular will fall from the 
A'^gle C' upon the Bafe AB, wbith is al- 
■ ways the neareft diftance itom C to the 
Bafe AB ; and then meafure the Lergth 
of your Perpentticular by yoor Ghaio, and 
having the PerpgndicuUr and Bafe, you 
know how to find the Content. 

How to Miafurt a.^va^xayguUr or Foiir fdei 

^ield. 

Fig. 88. "Let ABCD be a four comer'd 
Field: 1 beg;n as bclore at fome rematkable 
Argle^ and gdirg round the Field, I find the 
fides to be 9.04,8.75, 9.12,8, 17, and 
the Diagonal AC 10, oc, I begin to pro- 
tiad: iljus : 

I firft, bythehelp of (hj* Scate arid Com- 
palTes, draw my Diagonal 10, 00, from \ 
to C, and I.make a Triangle of it and the 
firft and ferond fide 9. 04, antt 8. -j^, as 
in the lafl Fitfid, and another after the fame 
method of, that Dia,gonal, and the third 
"and foruth fides 9. 12 ^nd 8. 17, fo have 
I the Trapezium ABCD. 

Then by the help of my Scal^and Com- 
pafles, I find the Length of the Perpendicu- 
lar of the Tliangle ABC to 'br ^. 90, and 
of the other CD A 7. 2 J, which added To- 
gether are 14 10, whereof the ^um 1*7.5, 
G 2 by 



1 24 The Toung Survejor*s Guide, 
by which multiplying the Eife lo, co, and 
proceeding as lormerly hath been ihewn, 
I find, the Content o\ the Field to be 7 
Act*»i oRoodS) 8Perchei, as here foltours. 



The Bafe 10. co 


y Perpen 


l-°'i 








5000 




7000 








7| 05000 . • ■ ■■ 




4 








20000 




40 




S I oooco 


Bor t» take fbi Hot 0/ «ij MtbanstUr 




FM. 



F/g. 89. Let the following Figure A, B, 
C,p,F,E, reprefent a Field» <^ which, the 
Plot is required. . i 

fvP, Meafure the Length of the He^ge 
AB 7 Chains, then Meafure the Length of- 
rhe Fence BC 6 Chains ; ai alfu from A 
to C the Bafe Line proper to that Xrian&le 
which is foiind lo, oos all which Wute down 
in your Field Book. 

' Then 






The Yoimg Surveyor' i Guide. i-^. 

Thn Meafure the fecond , Triang[le ia . 
the fame Order, beginning at C, and Mea- 
furing to P, which is found to be 3. 10 « 
-then Meafure from C to E ;. 1;, and Iila- 
wife the Bafe Line C E. 8. 00, which put 
down £or the fecond Triangje. 

Then obferve the laA Triangle, which is 
an outward Ao&le, and muft accordingly be 
Meahired on the out-fide of the Field, and 
fo qoted down in your Field Book v fo the 
Lengih 6i the Lin.- EF 2.15, and AE j.8o, 
ihe Bafe Line, and AF 4.00, all .which en- 
ter in Tour Book as follow^. 

F/Vjf Triargle ABC inward, 2, Trijinglp 



CED inward. . 






,G 


L 




C. L. 


AB 


7.0Q 




CDjdo 


•EC 


6.0c 




»fi!.i! 


AC 


0.00 




C E 8. 00 




• — — 






Third 


Tiiangle 


AEF'««wiid, : 




c.. 


L. 






EF s. 


IS 






F A I. 


06 






iAE!-- 


83 





Haw., tt Prolr^3 the former Work ttpcH Pjftr 

FirPj Draw a Line upon your Paper ae 
pleilTure, as AC, and take from^our Scale the 
Length of that ^ine, lo. oo ^ and ftt it 
' G 3 from 



I Q 5 The Toung Surveyor* s Guide, 
ftom A to C i then take ftomyour Scafe the 
L -ngth of the' Line AB 7. eo, and put one 
Faot of your Compafies in A, with the o- 
ther defcribe the Arch t a ; then take the 
L'ngth of the Line BC 6.00 from your 
Scale i placing one Foot in C, with the 
other crofs the former Arch in B, as bb, 
this done draw the 2 Line* AB and BC. 

S*co>ti, Take from your Sctle the- Bafe 
Line CE 8.0a, and placing one Foot of 
your Compafrfs in C, with (he other de- 
fctibe ihe A^th ee, then take wiih your Cem- 
pafTs the Length of the Safe Line EA 5.80, 
fetcing one -Foot in the point A with the 
other crofs the former in the point E, a»ff, 
which point' £ is the meeting A) gl^o both 
the other 2 Artg'es. 

Thirilf^ Fir the protraflionof the Tri- 
angle CED, take f^om your Scale the Line 
CD^.-io, i^acing one Foot of your <!;om- 
pafTe* in C, snd with (he other -malee the 
A-'ch cc, then take the Length of the Line 
DE 5. 15, and felting one Foot in E, with 
the other crofs the former at D,as dd, from 
which lnt£if.dion draw the 2 Lines CD 
and DE. 

L^ftlys For ihe Triangle AFF, take with 
your Compaffes EF r.15, ] bring tjue Foot 
of your Compalies in E , with the other 
ftriks the Arc ti hh, then (ake AF-400, fer- 
(ing one Foot in A. and »vith the other crofs 
the former Arch inF, draw Lines therefiom. 



f;oosic 



The Tput^ Surv£yor*s QuiJe, 1^7 
9s from A 10 F^and from F to E, foliave 
you protra£ted jour Plot upon Paper, as 
was ff quired. 

And you jnuft he careful to note down 
theSdruation of the AngUs, r»«. inward and 
outu^rd, for fear of oommit^ng of a mi- 
ftake when you protrad the fame. 

Now if you draw aLine from C to F, 
you divide it into 2 Trapeziums j, and then 
the Content is found as hath been before 
taught. 

Hav to fake the Hot of a F'uU. by g^iitg 
romd the fame. 

JFig.ApLit ABCD-reprefent a Field to 
be meafured. Firft beginning^ at the. Angle 
At I meafure one Chain iti Length towards 
B, 86 to q, and another towards £ as to b $ 
next, I take th? diftance from a to b i, 50, 
-and note it down in, my F-ield Book, t'of ' 
the Quantity of the Angle A \ and nieafure 
the Hedge i^B ;. 00, and put it 40 my Field 
Book. 

Ke« Icome to the Angle B, agd mea- 
foring one Chain tod, and another to c, 
I take the digance d c with my Cliain, and 
I find it to be .1:. 40, and the Hedge BC 3. 
1 5. Next I come to the Angle C, and niea- 
furir^ one (. hajo to e, ami another to f\ 
and ■ take the diHance f e, t fjnd ii to be i. 
ic, and from C to D, 2. 17, and fo, I pro- 
G 4. ceed 



>»3 The Toung Surveyor*: Giade, 
cefd till I come to the Angle A» and I find 
to be ai follows. 

C. L. C. L. 

A I. 50") f AB .3. 03 

B 1. 40/ ■ \BC 3. IS 



Angles 



C I. io>S;drt /CD2. 17 
D I. 8ol^ )DE2. 80 

E 1. 39J (EA2. 60 



How to Ptotroa the former Jf^otk. 

Tirfi, I take from tny Scale I Chain, and 
having drawn. a L..;i a> AB, upon A as 
a Ceuter, I ftrike ■^=^ Arch a b ; then take 
from your Srale 3, r.j, and fet it from a 
to b, and draw the L'ne AE, fettirg thereon 
?. £0 from A te E, and j Chains from A 
to B } then talcing one Chain from my Stale 
■and putting one Foot in B. I ftrike the Arch 
c d; neit I rake 1 CKain 40 Ij-nks, the Q,uan- 
tiry of the Angle B, and fet it from d to c, 
and draw the Line BC , making it to be 
in Leni^th 3. 15. Nsit I come to the 
'A')g!e C, and fetting one Foot in C, wirh 
the other I defcribethe Arch ef, then tak- 
ing I. 10, from your Scale, I fet it froffl e 
to *, and through tlie point f, I draw the 
Line CD in Length 2. 17. Nextl'cometo 
theA'g'eD, and always taking I Chain - 
from my Scale, [put one Foot in D, and 
with the other defcribethe Arch on % xh<sa 
taking 



The Toitng Sttrvejor^s Guide, 129, 
taking iChaio and goL'ofcs,! fet it from o to 
n, and the Line DE, which Line muft juft 
meet the end ot the L^De AE and contain 
in Length 2 , 80. if your Work be well 
done. 

I uiuft acknowled^ that this fort of Plot- 
ting of Pdr«!s of Lind that have many 
A' g'es,Teqnires not only mors care and pinsj 
but; better Skid and Memory than to draw 
Diagonals upon Paper, when the Plot is al- 
ready taken by theplain Table. I Ihall there- 
fore give you fome ways to help yoor felf, ■■ 
fo as to be oDt of danger of Mifnkes. 

One way is, to divide aMnltangularField 
into 2 or more parts, then might each part 
be meafured feverally, as if they were ft- 
veral Mens Lands parted by a Boundary. 

Another way, which much helps the Me- 
mory andUnderAanding, is to draw s rude 
Draoght of the Figure ot the Linda you ih- 
teqd te meafure, not only as to the iides, 
hat alfo the D agonals : Then meafure the 
Lines upon the Ground correfpondent to 
thofe on ths Paper, and fet the L'nei as you 
meafuie them , upon the Sides of your 
Draught, as if they were the true oni s, and 
when you have finiOied yoiu Meafurin|,prc- 
traa it truly, and it will do your BuAuefs. 



Ijo Tf>e Tou/ig Surveyor*t Guide. 

How to tek: the Plot of a Field from me Sta- 
■ tion ttikin in the ,mUle thereof. bi tht 
Chain. 

. Fig- 91. L't ABCDE reprefenf theFidd 
10 be plotted:, firft at K, I fet down a Stick, 
then Meafore one Chain in L^rgth toward) 
A, as K o, and alfo the L-'ogth of the whole 
LineKA, which note down upon your rude 
Dfai ght : N-Xt nifafurc one Chain in Length 
towards B, ill K p, and alfo the L-ngth of 
the t-ineKS; and n(?te it on your foul 
Pra tight : Next you muft meafure the di- 
fiance ber'A'iit o and p, and fo place it 
iloivn upon your Drau^c.' 

Andfol meafate one , Chain .in Length 
towards C, as fi.g, agd .alftj the Length of 
ihe.JL'be KCj ana' note it down upon 
my. Hide Uraughr, as alto fhe diflaoce pg; 
■And fo I proceed rpuiid the whole Field, ' 
and find them tp ht as. js^iotsd in the Fi- 
gure following. ■/..,. 

. iiw to PtotraB^ thhjt^t ': '_ .' 

Firft (ake from 3'out Scale orie Chain in 
L'-'ngth, thfn upon K as a Center, defcribe 
the Circlenpq RS;neittatc from ytJul* Scale 
2 Chains, tin L^ngthof ihtLine KA,and Htit 
trnm K to A N xt fake^rom your Scale 172 
Lin. and ittittrom o lil! it touch the Circle 
irHi,and through -the point p, draw the 
Line KB, making it to be in Xlengih 215 : 



TJge Toang Survsyor^s' SuiJe- '■■' ^,131 . 
Thentake from your Scale tbe Length of the ', 
Line pq 13;, and fet it froip p to q, and '. 
through ihe point q'draw^the Line KG, 
making it to contain in Length 3i 6 : Nez4 
rake from your Stale 112, itnd fet it from 
q to R, and through tjic point R draw the 
Line KD, and take from your' Scale jiy, 
and fet it frpm K Co D i and &) proved till 
you have finifhfd y bur Plot. I'^nd, Lafifyt 
Threogh thefcytral .piQii)t#, A B G P, ftfc. 
draw the. BQQndary Liocf' , - : 

Haw to'tjkt iht Pht of. a FUU by the plam 
TiibU^ at one tr more Stations. 

. There afe three ways for doing this Work) 
The firft. pexfortai tlje Work hj Mieafur- 
ing every Line from tfia In{lril3ient to the 
Angles, and is a good way, when it caa 
be flpn^. The :fe(cond d&es -it^ by Meafur* 
iiigpply the St^tioqsv Diflaoces, and is 
VQfy qiick, , buf iiot (p fore and ^xa6t a^ 
the qtherj yet if it t« maoag'd hy ^ 
(kiifuU Aifift , it .will come near . ^oougfr ■ 
the matter in many Cafes { as Meafuring 
for Mowing, pr Reaping Fields by-, the 
Acre, or in Cafe ot Law Suits, whep yoq 
cannot come nigh the Ground tobe.Mea- 
fuired. 

: The 3(? is by way ot Circiilatiijn, tVln- 
flrument being oft to be planted, and tile plot 
to be meafured by going roundabout if, by 
which thick W90^s or Bogs amy bemeafared, 
la 



132 The Tmmg Surveyor* sGui^e. 

\n alt thefe MethodB two things arc to 
be performed. 

1. At evei'y Angle whtre there is no 
Mark already, as s Tree^ or £»/&, ftc. one 
mud be pUced tfith s white Piper | or 
otie muft go from Angle to Angle. 

2. When ever yoa have occafion to plant 
vour Innniment more then opcr, yoa muft 
be ture to let it Itand jaft as it did the fitft 
time, riiat is^'for S%ua1ion, which if your 
Needle be giod, will perform the Work « 
but is not itioughtfufiicient without a bad:- 
fight and foce-iighr^ Now for the iiifi 
Method, 

To Uh the Btt of a Field at me Station; in 
tny part thereof ^ from whence jou may fit 
at itt AttiUs of Corneri. 

■ Ff;. 92. Suppofe ABGDEF be a Field 
to be meafured. Fitfl, Caufe marks to 
he fet up in evei'y Cbruer of it i then 
toake Ohoice of fooieconrement place there- 
in, from Whence you may beft view all 
the Angles thereof \ in which place at H 
plant your. Table (covered with a Sheet of 
tUott Paper J mm the Table about till (he 
Nttile^ftand ovef the J'fciwr M Luee^ 
and fo faflen it with the Screw-pin, that 
Ibe TibUffir nof^; Then placing your Index 
upon the Table, lay the Fiducial Edge 
thereof upon th? point H, reprefenting the 
' place 



The Toung Surveyor's Guide, igj 
plare of youp Station-, and draw a Line 
wuh yoor Coinpaffes point, b^ ihe fide of 
the Index upon thr P^tpei ^ which done, dt> 
re& your fight to B, (fiiU keepi}ig the Edge of 
your Index to- the point H) and draw a Line 
as before-, and fo in like manner direayouv 
Index to C, D, E and F, drawirg the Linea 
upon the Paper by the Edge of your Indei^ 
withthe point ot your Compafies, and fo 
having finilhed theiatne, meaiiire w-iihyouf 
Chain tbe^ftance of every of thof« Nfarks, 
from the place ofyonr Station at H, and then 
by the help of your Scale and GompalTw, Ctt 
the fame diflances from the point H, in ihe 
Ijines drawn upon the Table, making a 
fmall ^ick with your CompaHes point ae 
the end of ^ery one of l-bem ; then with 
the point of your Black-lead PeniHl, draw 
a fmall Line irom-poe point to another, as 
namely from A to B, from fi to C, trom - 
C to D, &c. fo (halt you hav» upon yMic 
TibU'tbe' exaa P4ot of yaar Field. 

To tjke the Hot of my Field at ofis Statm^ 
in any one Mile thereof^ from whence all o- 
' iher j4^hi may he feen. 

^'$■91 Firft,as before,fet upMaiks in ei ery 
Corner of the Field, as at BCDEFG ^ ibm 
make Choice afthe moft -convenient Angle 
fhfrein ^ from whence 3rou m*y fcefl view ali 
the refi, as A \ and having fizt-youi Table 
there. 



1^4 ^* Tamg Swvej/or's Guide. 
there, 'as before ii raught , apply the ladez 
to the point A, and direct the fights to B » - 
then draw a Lne Afi upon the Taper, aod- 
with your Chain meafurethe t-ength there* 
of, and fet it down by the help of your 
Scale from A to B. 

Then from the faid point A, turn yout 
fghta to C, your fecond Mark, ajid then 
draw wiih onepciRt pf .youi Conip30fs up- 
on the Paper theXine AC , mfafuring the 
diftenee, and fetiing down the Lergh as 
' you were before taught. 

In like minner direft your Hghrs to D, 
E, Fand G, and drawing Lines upon your 
paper, meafure with your Chain the Di- 
ftante of each of the fame f^oglts, from 
your StatioB point aV A, where your Tab'e 
H planted ? then with your CompafTes take 
from the Scale the refpedi,ve diftances, and 
vid fet them down from the point upon the 
fevetal Lines, and fo defiribe the Lines 
AB, BC, CD, D£, EF, FG,.GAi which 
will Piaflly reprefent the juft F gure of 
yoar Field. '■':.■ 

How to tah the Plot of a Field at two St<^i<mr, 
when aU the J^glet cannot befeen at one. 

It oftenttoies happei)eth, through Hills 

ot the laigenefs qf Grounds, that you cm' 

not from any one place of th- Field fee all 

the Corners hereof j in wliifb Cafe you inufl 

make 



The Toung Surveyor's (hude» ' 1 5 j 
make Choice of two convenient' places 
within the fame ; Sa that here you are to 
perform at two Srations^ what you did . be- 
fore at one. ' 

T'g. SV4.S ippofd rVr'^for^j '^at the Figut^ 
CDEFGHiKLM, be a Fiel^l to be plotted j 
I make Clioice of tw;o Stations, wittiin the 
fame, as A and B» where I can. view all 
the ADgles. Apd firft, I. plant my Tabic 
at A, from whence , I can fee the A'-glei M 
CD£Fi then plitcingi the jEdgpof iH7 In* 
del lipon the point A, I ii.iuii my fight* 
feverally to the Angles within my View, ai 
to MCDEF, drawing Lines, rg is direflsd 
in the F'gjirfli ]i((l)icli dpn?.,..I aieRfure 
every pne of ^eca with) 01^ Qhain ,- and 
n<4,i thdin ,doi|VA fr<>fn 'ny, Sp^Je^. -as 
forjT^alyp i >! _j , _ ..■:, ;.'•■■ i 

T.l)i^n (my Ta{>U' remaining' ^xt) t view (ha 
other p^rts ot the Fie^d, and make choico 
of (lie point B for.rqy feoijd . Station; 
becaufe from rhehce, lean fee all .l)j? 0theis 
AigIes,of the Fi^.i i^eo fettiijg up.aMirfc 
thcie, I go b^ck tp:n3y firfl SutiiJO 9t A^. 
(whiire mjTabhfivrds /«etf., «J lUfi it,) upott 
which poini l move my Iiid<x, till ttirougli 
t'le fights thereof, I efpy the M^rk atB, which 
done, I draw a L'neby the Edge of (he fndej^ 
with the point of my Compafs,ei tending ic 
the Length of ray Tabl«, as is reprcfeoied 
by the Line ZXj which being thus per- 
fcriaed, I meafure my Stationary diftance 
AB. 

n,,,.„..C(H)<;lc A 



. -rvO^ Surveyor't Guide, 
AB, 2 Chains which I fet off from \ to B, 
(he place of my fecond Station, by the help 
of my Scale and CompafTe!. 

Stcmiljy I plant m; Table upon the point 
B, and laying my Index upon the Line 
ZX, I tarn the Table about, till through th« 
fights I bshold my firft Statioir at A, then 
I Screw the Tiri)le f aft to ihe fraff ; after- 
wards moving my Indn 'Upon the point 
B, I direfi the fights to- G, "drawing the ob- 
fcureLine BG, containing i Chain 7?, then 
sgain 1 dirt-d the Index to the Angle H, 
«nd find it diftant from my Station i Chain 
72 t and tlnis tnming my Index abont up- 
on tbe point B, I draw' obfcure Lihes to the 
other Angles as I did befbre, And meafbr- 
ing tlieir refpeflive difian«> With-my. Chain. 
I prick down the points I, K, L, npon my 
Paper, ever obferving to lake off with my 
Compafltis upon the Srale the exaft Quar- • 
tity of -Chains and Links; meafured with 
Cbe Chain. 

: Lifffr, {The feveraJ pnttt9 or Anght »f tho 
field, m CDEFGHIKLM^yeir^Jbtrnd oBt, 
tad mark'd npm my fjper,) l' df aw the Boun- 
dary Lines from point to point, which will 
reprefent the -trae Plot.of tbe Field, to be 
Meafiired. 



To 



X&tf TVttfig Svrvejters Guide, 137 

To tah^he PJotofa Field r«mved from foUi 
at 190 StJtiom^ when you are not pamit- 
ted to comewitbht the fame. 

^» 9T- If often happeneth that you are 
.40 (rtesfiire a Field, and canno', either fer 
W4ttrr Mooriih Grmjnd , or <)anger of 
Suir, filter into it. S-ippofe the Field is 
CDtFG, I iUflkeChoiceof (wo convcnint 
Stations without ir, as A and B, from each 
r>f which I can fee all the Ang'es of the 
F.eld ; and having -planted my Table at A, 
1 place the E'ilge ot my Index thereupon, 
and direS toall the Angles of the Field're- 
ipeSively, drawing Lines with the point of 
my Compafles, as AG, AE, AF, AD, AC, 
AH. Then my Table remaining fix'd, I 
din^ the Index towards B, and having 
drawn out my S'ationary Lme, I n^eafure 
the diflanre thereof in the Field, and place 
it on the Paper from A to B, then plant- 
ing the TaMe at B, place your Index upon 
the Stationary Line /B, and then move 
the Table, till through ihe fight* you be- 
hold yoor Station kt A ; which being ef- 
fected, direct your Index-to alt the feveral 
Angles of the Fi&'d, as you did before at 
A ; and the interfedUons of thefe L'nes, will 
give the points C, D, E, F, G, H, from 
which draw the Lines CD, I>E, EF, FG, 
GH, and HC, and you will have the true 
Plot, and Frcpoifion of the Field. To '• 



138 The Tottn£ Surveyor*! Guide, 

To Survey Woai-lrnds bj the plain Table. 

In very irrrgular Groundf wher« you 
can make long Stations, you cannot fee all 
the Anglfs from' each Station ; but in go- 
ing 6a your Starionary Line, all the little 
cornets in the Hedges may be feen -^ tbtref- 
fore, that yoa may Plot all the Angles as 
you mpafure on your Stationary Linct, ob« 
ferve this G«neral Rule, vis. 

A. General Rule. 

In going on your Stationary Line, marfc 
where an Angle (alls in aRight-Angle to your 
Stationary Line, there plaiir the Table, lay- 
ing your Indei upon the Stationary Line, 
'■: and ttjrning your THb)e;H|)oh the Head of 
J^our Staff, till yen can- fee either the Sta- 
tion you came from, or that you are gor 
ing to, (for Tov miifi ahap obfervi to neafure 
in a fireight L»i^ from Station to Station, ) 
there fcrew it faft -, then obferve how fat 
you have, mesfured on your Stationary 
"Line, which diftanee take from your Scale, 
and place trom yoor laft'Stationary I-ine, 
there make a prick witli your Compaflei 
point, and there take the Angl.p. ■ 



-IZiEw Toung Survejfir*! Gmde, \ 39 

Example 

K^. 96. Suppofing ABCDEFGHIKLM 
N-^P, to be a greit Pool or Woo i : TI-QUgh 
there be Fifteen' Aogles, I ptapt my Tible 
only five timeg, vis. at :''EFH and M, and 
upoD the dry Lines A£, FH, H M, and 
M A, 1 raife their Perpendiculars in dpe 
places, (according to M^i^fiin) and alfo of 
a right heighih : By whicn and my five Sta- 
tionary Angles, I draw the boundirgLines 
qF the Plot, excluding, all the 7'^>a"g^'^s as 
foreign to ir, they being no refemblancefl 
^f any part of-the Pool, .but of Land ad* 
2^ent. That if by reafonof troublefomS 
9rulhTWood, Gorfe or Bogs, Cfc. I could 
not have rneafured clofe to the fides EF, 
Hi, or LM, it wwid be th« fame thing if 
I went parallel to ihem. And this is a ihifl 
that the P^a^ical 3<iveryors will oft be put 
to make ufe o^ 

Now before I pais to rmthet Varieties let 
iny Reader take oolice of thefe fcJIowing 
things., 
. 1. That it is ihequickeft way to mearure, 
fitft from the Inftrument to the firft Angle, 
Slid then back froiji the fr-corid Angle to the 
Inftrumenf, and la the reft in order 1, fiill 
one from the Inftiument, and the other 
to it. 

2. In 






140 Tht Toung Sarveyor'i Guide. 

2. In all working by the plain Tible, 
Tou mufl have a care that the Inftrumenj; 
be Dot moved out of its due place, till 
you have finiftied the work at the prefent 
Station, for which purpofe call yonr Eye 
now and then upon your NMdIe, obferving 
whether ir hangs diredlly over the fame 
pointy OB n-t it at whtnyou began your work, 
and to rfflify your InRrument if ^aa fee 
ciule. But becaufe all Inftrtimeprs have not 
Keedles, inakeufe of the following help. 

Whtn yoti have planted yonr Innrumenf, 
and made a prkk on your Paper, repre- 
feiiting your Station, fct the Edge of the 
Index to itand turning it foftly abbut till you 
find fome remarkable thing upon one fide of 
ft^the Cloie, and another on the oppofite fide 2s 
'••■' yflu look through the (fglw»ofypHrInder,an4 
draw 3 remarkablfli'ne quite overyourPapert 
then if you fufpea that by any accident thp 
Inftruinem is removed, you may eafily trjr 
and reftiFy it, bj applying the Indei to the 
fame line, and making ofe of fore-fights and 
bark-fights aE(»in , upon the fame marks 
which you bel^bre oblerved upon the oppo- 
fite fides Af the Clofe, And this i»a vJry 
good way when you plant your Inftniinefot 
lo the middle of the Fields ' , 

Ceiicenrhfg 



The Tomg Surveyor's Gwd»> .14^ 

Covcnmvf, ibe Phttirg of mttty Chfes tf^ftber, 
wbet^tbe Ground he even orwieven. . 

^S 97Sstfppofe.ABCDEFGHlKLM to . 
be a Tenement or fmall Detnefii dtvitled 
into 14 Clofes, to be meafur^d and prc- 
trafled according to their fevtral fhapes 
apd Stituation. I firft draw the Plot 
of the whole by the method of CircuIatioHi 
this being done, a Line from A to C gives 
the Triangular Clofe ABC, for the firft. 
In the next place, tgo round the (wo Clofes 
■ beginning at A, then at C, and fn about 
to A again : And then for the third Clofe, 
I plant my Table at p, and go round to C, 
rhe line CD being prorraded' akeady, an^ 
fo of all the reft, flillobfetvirg which are 
comnioB iiries belonging to feueral CloJes, 
that yh\i may avoi3 the meafuring of lims 
iHore than oncp, and l^y every parr of every 
Clofe in its du? place; that you befiire (o 
keep (he Inftru^ent. throughout the whole 
work to its true pofitioiiby Keedle, fore- 
^ght 'ind back fight. 

Theri' are I confefs divers other ways of 
doing this work, but none more fare. . 

2. If you are to makeaMapofaLordfhip, 
.walk over the Lordlhip '2 or 3 rimes, nl! 
you can bear the Map of it in your Head, 
that you may the better conceive to carry 
on the whole work, and to make choice o€ 
the 



142 The Toung Surveyor*s Guide* 
the fitteft ]tlace for your Stations. Plot your 
Townfhip firfl:, beginning in the mnrt con- 
venient place to maki; your fitff Station as 
long as pofllble.youcan ; and Jik^wife from 
your main Stations, taking therefrom all 
Oat-Houfes, and little intermediate Officfs, 
and then return to your meaa Station a- 
gain. 

Ohftriti thit Gtneral SmU. 

When you cannot perform from your 
main Station, or fee all the Angles, or Back- 
fides near joinirg thereupon, to make inner 
Stations as before, and to perform the vTorfc 
of each main Station with inner Stations, 
till the TpwnOiip be finilhed. 

And where you conclude your Town- 
fhip fromTour iaft main Station, direft your 
fights to a Station in fome convenient place 
of the adjoining Fields j fo may you take 
the Plot thereof from as many Stations as 
need requlTes, fo will fuch Grounds be join- 
ed to the To'wnlhip, and fo may yoa pro- 
ceed with next adjoining Giounds. 

Your Townfhip being by the preccdii^ 
Rtiks cwnpleated upon your Table, with 
as many of the adjoining Grounds as will 
come thereupon, make Marks upon your 
Plot as you proceed with yoar Work, 
where the next Ground joins or falls upoii 
tfaofe Fences you have already plotted. 



The Toung Surveyor's (juide, 14; 
that you may Jcnow, wheayoi^ve raken 
the Plot of the feverab Fields joining up. 
on your former Plot, how to join them 
therete. 

Proceed where you left ofF, and take as 
many of the Incl'oftires upon your Table at 
it will bear, and join them to the foimer 
work, by the diredions of the Marks befon-* 
mentioned ; and in this order proceed till 
the whole Lordlhip be fioiftied, obferving 
to. dtfcribe upon your Plot all Roads, and 
whatever is remarkable that you me't with 
in your way. Obferve to place the Trees, 
in. each Htdge>Tnw, fo that the Landlord 
or Owner (hereof may know by infpeding 
<he M»p what Fences belong to eaih 
^Gtonod. 

The trve metboi of takh^ the Plot of Toteven 
Hi9y Grounds, in rfJpfS of their trm ^um- 
tity^ by the plain Table. 

I. InGrounds wtore tbare are multiplicity 
of Hills' running oat: into apother Irregu- 
iarly , place Betcbni upon ferveral 'oF 
the Hei^ft ot the mnft nwterial Hills, 
whether you can ffe the Angles in the 
Hedges, or (he Hedges themlelvra from 
ldv«ralofthe filid Hills, and direfl yoar 
^hts from Station to Sraticoi, laying down 
each Stationary diftance upon your Paper 
with your Scula , placing :yam Sratjon' 
Marks 



144 "^ Toiing Survejfor^s GuuU, 
Marks fo, that ytmr Ch in in mfafating 
(hefe Stationary diftancts may pafs over 
(he mo/l materiil HiUs in the Giouad, as 
we fhall here demonflrate; 
■ 2. fV^.sd.Admitthe Figure noted with AB 
CDEF, f^c be a Hilly Ground to be. plot- 
ted, whof: jsft number ot Arrfs is rtg'iired; 
fi;t up Heacons or . Stationary Marks apon 
the (Op of moft ot ihe nalecial Hilla, as X, 
W J, 6 y, z, *, 

3. plant yrcr Tafele at X, your 'fitft 
Station, direding yoilr fights therefrom,- 1* 
the Angle Di then with your Chain mea-. 
fure the diftance X D on the Ground, vrhich 
take from your Scale and fet trom X to D, 
where make a'priclc ; tb^n direQ your fighti 
Co E, which diflance take from your Scale 
and fet from X to E ^ then direfl; your fights 
to F,- Whiph "prick off ffom X to F on the 
Papft } then again direa your fights to G 
and H, and mfafure the Ground Xjne8,urhich 
ftt off upiJH your Paper ? fo have you 
finlflierf (he work trf your firft Station. ■ 

4^ 'DxfSi'ihefote yov alter the Table i at k 
fiords planted at the fi>fi Station) your, fights 
to your feccoid Station at W, driwing yoai 
Stationary Line by (he Edge of your Jndezj 
and mekfure the Letigh of the faid S atio- 
nary Line on the Ground, which take from 
your :S^al% and fet from X to W, where 
place down yotir Table, laying the Edge 
of your Index apoa the SratioQwy Line 
XWj 



The Tbung Surveyor's Guide* 145 
aCWi yoDriodfxri-ft ng in this poftiirei^ turn 
*he Tsble gentty-qpon thetkad of" your three 
JLegEetl Staff, till through theifightsyoa 
fee ttie lirftSiation iraijcat X, where fcrew 
itfafti then direftyDnr fights to all your 
ftreral Angles in view, is K,-L,M, and mea- 
tiire their feveral diftances trom your Sta- 
tion at W, . wfeich feveral diftances lake 
ftODi puf Scak:and prirk off upon iheir 
Rcrpe^pe Lines, ppan your Papen. : 

-y. '. Theri" (to b'efote) dirtft your fights 
to 9 ycui Third Station, and draw a 
Line by ihe Edge of you. Index, thej, 
meafure on the Ground from W to cf 
which take from your Scald' and fet-pnyout 
Paper from W to J, where plant yoae 
T^le, as ! wai before directed, at your laft 
Station; ' 

Now, becaure you nmnot fee your Fencffl 
in any part of the Ground by reafon of 
itie Hill fi-otn this Station, therefore di'rea 
your fg^ts to b , ymir fourth Star jon,which 
diftance S ft, nieaftre on the -Ground, which 
take from your Scale, and fet from ^ to 
.*r, wherfr-plant your Table by the former 
dire£lions, nd drrea your fights to y, yout 
fifth Sration; then meafure the the Sation- 
ary diftmce h y, which take from yoar 
Scale , and : place from h to y, wherft 
plant yoor T^Ie. 

■ 6. Then direft yotrr fights from your 

-SiatioQ at y, and therefrom ob(erv«, mea- 

H fufe 



^6 The Toung Snrvey^r^s Guide. 
ire, and \*y dourn apon yoar Paper, ai 
ou were directed ar your other Statiofli % 
Mn dire^ ynur fights to your fiidi&'aiioii 
'. z, and ftfike a Lineby the Edgt^ yoar 
idez for your 5 ationary Line, wTiich tak« 
oin youi Scale, aad fet from y tosVivliere 
lant niir Tabic by the /tiregoing dirf£ltonF. 

7. . Vout Table being (planted -M z; direct 
our fights to all the Angle* ia vkw, and 
rike Lines by the Ed^e of your Uidu 
ier«to, astoO; P, Q, R,fi,T, asd c?ca- 
ire tbeir diftances on (he Ground from your 
lacxof Aanding; which fcveral diftances 
ike from youi: Srale, and fet itoen Z, to 
>, P, Q, R, S, T,- whtre make pricks with 
oar Compaifes point \ whith doae dire^ 
our ^ghts to ynit Tti, or laft Station* 
rawing a Line by ih« Edge of your Ind^x 
>r ih« I^Srationary Line; then meafure 
e diftanoe Z * % which take from your 
ale, and f«^t from Zto *, (aa before uuglt) 
here plant your Tnhle i which done, di- 
a ycur fights to the Angle N, which di- 
nee raearurc on, the Gtourd, and then 
CB from your Sc&le and fet from * to 
where make a prick ; fo hav« you prickl 
' all the A^gles in the Field, 

8. Lajily., From the feveral pritks, as rr-ini 
to B, from B to C, and fo to D, (^c- 
w Liies tliei'efrom till yoti come again 
A , which fltall include the Motmtaioaus 
Id : which was required. 

And 



The Tou^ Sttfveyor^s Guide. 147 
And here you n^ay obferve,that the Chain 
1>eing drawn over all the Hills and Dales, 
muft necefTarily produce a larger Plot, vis, 
more Ground, then giing round abcut the 
Hedges all the way upon Ivvel or even 
Cronnd ro plot (he fame : Hence I may 
affirm,that ihisjway ought to be pradifed by 
&irveyors j from which ^ap the true Nun> 
ber or ?cm is found tfiat Jhe faid Ground 
contaiileth. 

CMcmihis Shiftily of Paper^ 

U vtty ordinarily fella out in praflrcev 
■wiTh your Table, as it is covered wiihPaper, 
is too little in feveral Cafes, e^cially in 
gceaf. Grounds ; in fuch CaOs when yoa 
nave proceeded as tar as you can, till the 
Lines tun off your Table or Paper, you 
muH ibi't your Paper, and put a fair fheet 
upon the Table. 

, Firfi then, upon your laft Stationary Line 
which runs off yoar Table, obferve to 
fliift that Sheet fo far off or befide the T^* 
ble,that yoor laft Sution marked thereupon, 
may be ma(k<:d jtiftupon the Table to u^hi'^h 
Sheet in this order glew a fair S'lset with . 
Mouth Glew, and fo faAenthem down with 
the Frame of the Table. 

Second; hay a Ruler upon that part of the 

Stationary Line^ from the Station, which as 

t faid beioce. ii juil upon the Edge at the 

H a Table. 



■I.4S . The Toung Surveyor'' sXju'uHe. 
Tablf, and draw or augment thiit Line oh 
the fair Paper, upon whith Line prick off 
yQiirSiationary difiancc 

Tbhd^ Upon this Stationary Line I37 
-lite Edge ot your Index, then tot n the 
Table upon the Head of your S'aff, tiH 
(hrough the fights you W the iaft Station 
,yriu direded-ioi lo will yJiir Table be 
jTydlified to proceed with your work. 

£xatriple_ 

Fig. 99. Admit the following Fig'!re G H 
JKLMN OPQtRSTU WX, reprefent 
a Field to be plotted by the plain Table, ' 
fwhich is To ]ai,ge that it cannot all be plotted 
«n the Table ^ and becaufe I would - nave as 
much upon theXableas it will bear, 1 be- 
gin 39 una the tt'.ge of my Table as I can } 
let us fuppofe (lie Tatjle witfitn the 
Frame to be underftood by ^ the Line 
•YA, therefore J make choice to begin at A, 
planting my Table there, and direSing my 
■Jiijhts to F i J mcafure the Stationaty d;- 
^ance /^f, which is almofi: the Length 
of the Table ; then I come bade to my fiift 
Swtion, and tliere again pbnt my T^ble in 
-fhe fame poflure I did at fifft, fo diredfcing 
the fights to B, taking (he Angles by the 
,«wa>', then to direi^ my fights to C, where 
*J plant my Table, taking myAiigks there-' 
Irotn ihat are in view .j next I direft the fights 









li«*>--l 



The Toung Surveyor's Guide: 149-. 
to the Station at D, drawing.a Line by ihe 
Edge of the Index to the farther end of ihe- 
Table,as Cd, where- it runs off ihe Tablej, 
then becaiif^ I can proceed' no firther before 
1" fliift my Pipfr, and put a tlean Iheet up- 
on the Table ; I take this (heet off, and witfii 
Mouth Glew, I glew another fheet to, it at 
TY ; then I put thsrn both together upon- 
(he Table in this order^ viz. I bring the 
Station C, to the S.'ationB, upon the Table^, 
and fo fallen them down with the Frame^ 
To that the line zz,. poffefTeth the place of 
the Line AB^ fo that part of the Plot iS' 
yet upon the Table, vis.. from-C to e, and 
. the reft of the Table being covered withfair 
Paper j^then plant again your Table at the 
S;ation C,, laj'ing the Edge of the Index, 
upon that part of the Sranonary Line, which- 
was drawn before your Pjp;f was fliifted, 
tf/z. C e, and extend it to D, upon your 
fair Paper, and then proceed to finiihyouc- 
Plof. 

Note, There is another way to- perfnnn- 
this work, viz. !y the Scales-of equal parts; 
upon the Frame of the Table, whicii is 
taught in feveral Authors. 






*'50 The Tetmg Surveyor*! GuiJe*. 

Xo taie the Plot of my Cbamphit FuJd -zcattaitt-. 
hig 20Q0, or 5000, Acres of Grotiftd, by the 
plain Tdble^ and jet never hejirced to cbangt 
' jour Faper, 

Too muftinthisCare place youfl'nfTroment 
ift eveiyAogle, and fo get everj- Arg1e;antl 
i(s Sdrs, not regarding the Length of ihe, 
containing Sides, as you ufe to do, then 
muft you msafure every Hedg, and as. 
yon were wont to lay the fame down 
by your Scale and Compafles. Here you. 
ihall only write the Length of erery Hedge 
upon the Line? drawn upan your Paper, 
and correfponding ihereunto, fo have yon fi- 
nifttd*, and you ffiall never be forced to (hi ft 
your Paper, nor have the L'nes to run ofF 
the fame ,' for you may draw them as 
]bng, or as fhort as you pteafe. i4iw when. 
y.>u come home, Upon lome ftieetof Paper, 
prdtraft all the Angles one after another; as 
y.iu found themtn the Field, altowirg fcy 
your Scale andCompaffes every Line its due 
Length : According as y.iu find the fame, 
note thefcFigurcs upon the faid correfpondent 
Lines, and you will produce a Figure like, 
and Proportional to the Field propofed. 
^\)\i is moft excellent for large Champion 
(^oupds,. and therefore worthy of Note. 

Bom. 



The Towig Surveyor*! GniJe, 1 51 

fiow to .hiom vhether a Flot be truly taken, by 
pi oviyi$ the work tit every Station ; a«i in 
caft of Errors how to fnd and CorreS them^ 
before you are too- far yafi them ^ by tbt 
plain Tahie. 

• Firft^ In -tfie i^Ottii^ any Field by the 

Slain Table; beliKC to; lot your Statioa 
Urics ftand »p in eteiy hole till you 
have finiflied your. Ploi 9 and likewife 
Marks in raottof the nraterial Angle» 
of the'FiftWi .«bkh J!7 rhe following 
diteaons will inform you whether yoo 
tatE-dbtwr-ght'or-iiot; andin CiTiot an 
Errw cbinniiii«d,,;howi.toiind wlwre it if. 
! iStcfflfJ; WtewyoHarBdaparttdfromyout 
£rft Sration, nid- (five prceeedrd to yoMt 
UxxtnA, and taken all your Angl« by 
the.wa/, and* planted your Table ac 
yaoi'^ond Sfxt^im, in- ordei to proceid to 

Sour third S^atiisi , .arid would kiacw wbe< 
lei iRe work of yoiff^ifl and', fecorid S*a- • 
tion be' right or imi : Direft your rg'^is. 
to one oi moreof the mofi m'sterial An^tles 
fton iotk, tK.yeu pnoc^dcd frcm your f\ (I 
«o yonc.ftcond; Staflioi); znA if- taeEdge- 
bf jDUBlndfaEtHt the Anglesupon thr Pinr, 
jTMi worJiiis'^fo: far tialTr taken, :otherwi£j 
not. 'i'" ■ 

Tbhii When you hawplantedyoinTible- 

at yoor liucd ir'ation, and t-dkea all the 

H. 4^ ADgle» 



i$2 The Toung Siirveyor^s Guide* 
Angle* \,y the wayj then dirffl your fight» 
10 your firft Station i and i* you find (he 
Edge of your Indeifo cut your firft Station 
upon your Plor, youi wrak isfiaflly per- 
forraed to your third. Station, where you 
then are : But in csfe you cannot fee your 
fifft -Station mark from your third Station, 
er place of fianding, thnD according to the 
hft Rale of direflions, diren; yaur. fighli ti^ 
fome Angle in tiie Field whidi you< have 
taken upon your Blot, -and if the: Edge 
of youf Indei, cut the fane Angle upon 
your Pbt, yonr orosk is righc^ otheicwife 

BOt; . , 

P(mthXiktvrKe.v/)nn yonj Table isright^ 
\j placed or planted .at'yoar fourth Statlp 
on, and all the Angles betwixt your third 
and founh Stajion, beir^ taken, ca& youz 
Eye into fbat pact of ctie: Field . yon have 
plotted' I and vie#~ which of yotjr Station 
Marks ~yoiB.caa fee( t\\ss you ftre already 
tome Fcoait. toi£i..'.eiihar firn orfd«ind} aa 
fuppofe you'could fee only :your feccno ^ 
S'aiion mark, then dire^ your £ghts from 
your fourth Station, or place of Handing; 
to yooF- ftcond Station s, and: if dre Edge 
of the Index ; cut the fecond . Sfatioa upoo 
the Plor, your work it iaiat performed 
right,. otherwi£:' not ; and if at any tiinc 
you cannot fee fome one or more of your 
Beacona oriBtationBCjr marks, befides the lafl 
you can« fiom,ihat yon have already pa jTed^ 

. ■. then. 



The Toung Survejcr's Gtiide. 1 5§ 
tflf n nuke afe ot fome AngIe,to prove your 
Plot hy^ as I fsid before j and by obferv- 
ing this Method, 'tiseafie to know whether 
yon have committed any Error or nor, and 
a you have, how and fpeedily to find'it 
before you be gone far pafl it^ which is fo- 
plain and eafie , . that it need* no farther^ 
Demonflration. 

The }>ej{ vay ofMijJinit^ the fever ^l, avi par- 
thttUr ^atttites of Arrable-Lmis ^ ^^ty 
and Meadovs , ^ivg-w the open or comaiia' 
Fielii!, vitbp'ott DheSiom for the taidv^ 
in and inclofittg a hordjhif. 

When the Sarvcyor i» to proceed abnufc 
the Survey ot a Lordlhip, or Mannor, 
wheretn the Lord 4nd Freeholders are z~ 
greed to improve it, in laying each Mans^ 
Land together 1 it will be convenient to- 
begin at one fide ef the Field, and there 
fet down the name of your 6rfl Furlong ^ 
IB a Etook of a> Qiiue of Paper, where- 
in each .Page is ~ divided into fix. 
Columns, fo as the two firfl towards the 
X-eft-hand fhall ferve the Breadth of the- 
Band at each end; the third or greater " 
Column, Iliall ontain the number ofeveiytr 
Msna Lands, and alfo his Name ; and the 
4tb, 5fA, and 6tb, for the reduced Lengthy 
Breadth, and Qtjantify<^ 



i^J4 7fo Tdung Skrwfcr^ Guu&, 

Neit afrer you have thus done, andare 
coaif to ihe Fmlong where you began, «- 
prefs in yMt Boolcthe Nitne of jrourEidd, 
and ihe Furlong ; then in the middlemen, 
or greater Column, note down tbe Kama 
of the Free-holder that firft begins if, with 
the number of hit Landi^ againft which in 
(he two firtl Columos towards the I.eft4iand, 
wricc the Breadth of the Lands at each end^. 
nnd in the three laA put the redaced 
breadth. Length and Q.u3ntity; which 
done, fttt down the Hjme of the Free-holder 
that liei neit, and the number of his LamfSj 
together wirh the Length, Bteadth and q'jan-. 
(iiy, as before, and fo proceed in order 
till fou have finifhed the Fiirlong. 

And To on from one Furlong to anor 
ther, till you have finiflied the wbola- 
field. -■- , 

But that you may the more fbll^'jiadex,-' 
ftand the Form thereof.- I ftiall' Dieur jrtm 
iin (be following Example an sb^o- 
hire Method ,. how you may rffefl th» 



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. Cin><;l.- 



After ihi< manner you are to praceed 

ffom one f iirloog to another, until yott- 
have finifhfd your Field-Book ; whicb,be- 
ing done, you are next to make a particu- 
lar ^f> -every Mans ,ArraUe,'iLeys. ai>d, Alfa- 
dows feveiaUy,: to wh^kh pufpofc,' upon a 
&ir {hee^of Paper, y&uafe to make fa 
many Columns , as there are Free~- 
holders , every one whereof ia -to 5e 
rufadivided iattt liine, .Ib'wil] the.firftferve 
feit, Arnhtei ^di& feeand' :;for Ley! Ground, 
afid ihi third andr UR foe Meadow, if 
di^re be "any t And if oneftieet -will not 
contain the whole, 'then may you-tjike two- 
Off. three,' or fo 'mani^ as you Set coi> 
nribieBt..''- ■ .- . ' 

.Nets ym^.-3i«tii take the PIot,'i«ld~ gr>. 
Beralfiurfie}'' oi'.the whale, accordit^to tha- 
RaJBf'. be'bre dF^ireretd, land fe^ if t^e Suifi 
rtf-aDlh^'Edttfcalaffe agree with the Totai, 
t&en ydu.may couelade the work is^Ngbr, 
bnhf ^oft-conuoonly the I^rticubrs willi 
faine#httte2!ce(d the IBeueral Survey^' and) 
i^-:'diis.'.6are,' t^at: both 'may agree, you- 
arbtibiiredtiratlie Satmitf i-veiy Mastf ?ai- . 
tfliubrt anfttKKabte to-'the'-Proportionbf his^^ 
QoDund, whkh may b tfiefied by the Gol- 
den Rule. Far, if in the whole Eield 
fi^nciurdinit it be- loou Jcrtr/tht Particulars^ 
exo'eed iNe: Ofeuerai. Sferwey g'Acrefl,! .whut 
B\3ii]:^oiJic^ei}'liit,ji^Jh'nivfHi\be, 8 Psrofans,- 
aod & il»i(:ti£:.asf lo detlna out-ot theSum^ 



15^ T£* T^ung Si»v^f^f<^itfy* 
Totflt of flich a Msn» PafttcnlBn^ acoofding 
to which lam to Plot him t^AcKs jRouIf,. 
32 Percbce. And fi> of the* reft. 

Bo9 to tale tht Phti>f'd J^Hfr'oih- me 9i*- 
tStm tahlH ht the mSdU tiKivrf, hj. the' 
TbeodbSte-y or kf the Bigre^t on-- tb» 
glaht Tahie. <. 

%. locLet ABCDm n^^nt the Ftgn^ 
of sField tabr pIbttedbytfaeplaioTdble' 
in Rainy W«aihet. - putod thd £rabM--: 
wilhdor a Paf^r,: .tbc gridutcd. liile.^p-' 
wards, and plant it in fame ranvcnieiU' 
place, whence 1 ran k* all t^e AngJes, as. 
at Qy then Blaring the Index upcn ^tJ. 
Tablei^tbatitie^fidudal Edacckitb tf' ifw 
(acae'tinw time <go ihtougfit tba Center vp^'. 
on .the 'Bible, and tfae.linnitrpoiithfrFmitvt- 
of the Table cutting it Peipoodichlatty at 
^^Qy (.vbert tht Dorset b.^gm and. end) and 
i,^o(tbsax»B £r<i/^^ Ifnrn aboDtthe TaMe 
upon the &aff heady till thiiotigh the 'Hf^YA^ 
(tbefde vt«rkei:with iSa btiiif^ neah-iUhte. E^e^- 
tfee the Angk A, and theirs £.-i*Br^itfeft; 
obferving, where tay Needle eotteth, I'^nd'- 
by harlcfight-oaufinga-Maik tatefetuffcin- 
tlle Bine CD at ihc point E, tliat the in^. 
finimenftnvy beJupc iirni tI»mv^mobntg^ 
\,or. h r^ftdif , a k notKj^Xdunrg-thcd 
Work ''A|ld.d<MVJhe'l^ibe^Of^p8i^liIlgltp^: 

UOdcB 



The Toung Saneyor^s Gutt^ t Jgc 
under . the fights of ^« InflnitxKRt to the 
mark at F, is ("j it were) the^prime Dis- 
meter whence the D gree&of the Arglea are 
to be numbred, and accordingly 1 matk; 
the Aagie A^ in my Tai>k hereafter to 
beeiemplified with ^£o Degree*^ But tq 
proceed, tmnang' the Index with tht fi- 
ducial Edge Dpon the, Center, til) J £ee 
that Thread ratiitig the Mark at at B, 
the &id Edge cats upon the Frame at 76 
Degrees t; Minoitesr 1 note downfdt thai. 
Angle : Tile like work I do, tm-ning (he- 
ights to C,E1 and. E, (but not to F, for thert 
it no jitigle but only a Mark in the Bouniatyy. 
and i find mine Index, to cut for, every An- 
gle as Ihave Marked the[n,withiB the prick- 
ed Circle of the laft Figure, w». 157 deg.. 
«. Miootes for C, ' 225 degrees 20 Minute*. 
ipr D, and 27% Degrees aad 5P Minutes 
fiw E. 

Then I meaftffe (w cmfftohpilthf mM-- 
SueJ.: bf othirt) the di&ancei- 
Tirtwixt the place where ;the _3^ ''""'' 
biflruinent flbads; and ev» |_L?_I 
igr Angle, and fiid them to A|3io| 
lobeasIbiKretthftnupai'^ 1^^; 
the pricked Linei in the little ( dII,^ !o 
QkIc, mV a 4. Chaiui 20 [eU?*! , 
- li^nks, B 4 Chains 3 Ijyiks, I 

C 3 Chains 8^ L^nks, D 5. Chains 35; Links, 
C ^ Chains 6 Links. And now my Table 
hotlL for Lines and Angles is ihiu perfedl-- 



iitfo The Tmmg Surveyor*t GmJe^ 
ed, and the work is ready foe Protra^ioD 
irirhin DoorF. 

Now to protrad our Obfervatioix : Idrav 
upon Paper a Line A F at rtdventurr, 
fi> it be long enot^h, and (lick a [nn in it 
at pleafure tor the Center O, upon which 
I' place th« Center of the Pro(ra<5):r>r,. (a_ 
that -the fireighr fide of the Crolrador majp 
lye upon the Line AF*, the Limb or Arch* 
edfide being upwards towards B^ hy the 
help whtreoF I make b prick on the Paper at 
•^tf dfg. 15 Mill JorB, and at i;7deg. 55^ 
Min. tor c, accoiding to.the nambm in my 
Fie)d-Book. 

Then turnitig the Ptorra&or aboat. the 
pin, with the Litnb down towards, I) and E„ 
till theDiameter 1/c again juftnpen-the Line 
AF, I nambef downwards (rom the Right- 

' hand' towards (he Left, beginning 190, 200, 
€5*^. And ove-ragainft the place where 225: 
digrees 20 Minutes and 278 degrees yo 
Mintires fall, I prick the Paper at the £de 
q\ the L'lrtb, and thfoagh thofe fow 
poinW. I.draw i^a mJny feveral Lines^; up-- 
onwhich,an!l alfoiipon tfieL'.ne A O, Iimrk^ 
out by points the- (rue nieaiiMe of nVAty Licet 
fa^a Scaleitroni theCenrer, ami from thofe- 
point§ drawing the £ines AB» EC, CL), DE^ 

ud ££j I have the tuie Piotof tlie Fipid. 



The Totmg Surveyors Guide, tSt 

H't" to Jiihe the plot of an, hrsguUr FieU hjr 
the TTjeodoUte or liy the Dtgrees cti the plaiu 
Tabkbygoir^touvd the fame ^ being the beji 
M tbod hi PraSice. 

i"^. loi Firft caufe marks- to b« ftt up at 
every Station, » A, B, C. D, E, F i tVa 
inalcing Choice of a Station at A to begin 
at:' Meffure from A; to th« Hedge at 
a, which you'll Cnd.to.be ^5 Linksi wl^ich- 
Dote down in your Eye draught cr Field 
Book y likewife mcafHre from A, to tho 
Hedge at b,|ind you'll fipd it to be 20 Links^ . 
whioi Note down i then meafureirom yout 
S'^atipn At. towards B yoar fecond Staiioir. 
.ftP^ ^ f c- ;4P ^ .■yow have an oS-f«t of 
jo.Li'nkatoi the right at the corner c, and 
- at Sc.^aKyoa have meafuced to your fecond 
Station Bf B) where you are to fix your In* 
firi^nent 9nd take^the Argle AB'J, which 
V-fo^r^ ta;be 12^° jo.' which note down-^ 
^p meaiure from your Station -B to yoor 
StationC: i^hich contains. ;c. 2j/.atSt^ioH 
C, meafure to the Hedge at right Angles to 
di whichletbe-35Linki,and fromC to the 
Hedge at e , is zo Links , fixity yoos 
loftlttHKlU at C take the Angle : BCD, 
which cppiaitisj 104* q'} then meafure is a 
ftreight Line from C : tawardft D, ainl at i c, 
70 /. you have an off-fet to the Ccnrner at f, 
which contains 3; Links; at 2c. ;of.you 
bare an b0'-(et to the Corocr; g : which is 



1 6i The Toung Surwyor^s Guidf, 

I f. 20 /. at 3 c. poil you have another, at )h 
of I c 40 JL then oieafuring on 6 c, 30 J. yoi 
are come to yooF Station Di mature from 
D to the Hedge at right ArgUs to i, 
whichia 80 Links, and from D to k : whicb 
ii 50 Linkii Th«i fiivfiur InllnimeBt at 
D: andiakethe Angle CDEi whichisy?* 
30' : Meafurmg along tfie lM\i DE, vooll 
find that at 3 c. 60I. yeu have anolf fet of 
1 c. 50 1. to the Angle at Ir and at 8 ?. j"57. 
yon have an cfF-fet of i c. 50/. to^he Arglt- 
at m : asi at 1 3 c. 20 !■ you ha^e meafured 
10 yourStationat E: froni E to the Het^e 
»» T^t Angln meafiire t& n : which ii ;d 
L'nks.and fromEto 6, wM<his ^o tinfts at- ' 
fo: Thmfii your rnftrumenf-fifiatE,.and 
take the'Angie DEF, ■ vi'hich i* f9' ^: b\ 
then meaGiringina iRrfight line fioniE to- 
wirds F: you'll find that at 4 c .• jo t yoa 
. tonch the H*dg«, and at 8 c; 3c»-I. yon liave 
incdfured to yonr Station at F; Fffiih F 
Mtbe Corner q, ■ Wright Angles conraibi 
53XinkSi--b#cawfi: you have meafiireJ'^to 
the very Corned, you have no occafTon M 
meafiire from the Sratitm F , to the Hedge 
af.r; Having fiit -yoot Irifirumerit at F r 
lalte the Angle-E FA whichcdntafms *q 8" 
St/ then me^furing'frdm Fr tpwilds A 
yda'll i]nd<rhat at -2 c, '70 /. you ha4t an off- 
fet of 8y L=nk»rffrh'e'bend af S:' rfiMl rt 
6tf. 65 J -yen have mealwred to -youf firft 
Sration at A ; wJBie yeu began. 



Jhe Toun^ Surveyor's Gaidt. itf j 

Nov toprotra3 tbeje Ohfervatiaii:.. 

Firfi draw an obfcure line at pUafure, at 
AB,then with your thiDB.aIer,having 27f qual 
parrtinanlnch plaeed upon the very Edge 
(hfitig tht Kumher that this Brav^ht ip/w yro- 
traSid by) appFy the Edge 6f this Ruler 
to the L'ne ' AB, and with your protraffc- 
ing pin make a mark at 3; Links, from A 
lo a; then place tfic Edge of your Ruler at 
tight Angles to the line AB, and prick oft 
so Links from A to b : then phce the be-' 
ginning of your Scale at the point A : tfii 
Edge l«ing laid alorg the Line AB, by 
your Field Book or Eye Draoght you'll find 
rfcat at 6 c. 40 f. you hai'e an off-fit to the 
Corner c: which accordingly prick ofF, and- 
drivr-lbe Black-line be, then at 6c. "jot 
prick off the length of the Line AB; at the 
point B,- with your protraanr lay down 
•he quantity of the ArgTe ABC 126"^ : ?'b, 
^nd with Toar thin Ruler prick off upoii 
the Line BC 3 c. 35 from B to C, at the 
Statioil C: prick off 25 Links to d, and 20 
' Unks to c : both being at right Angles ^at 
Ihe point C : Piotia^ the qiiaittity oP the 
Angle BCD 104' o', then with yonr Scale 
firiik off npon the Ime CD I c.yol and at 
r'ght Angles to thfs point prick off 25, 
Links to the Hedge at f : Then draw year 
boundary Line throagh the point f and e.* 



1^4 ^^ Toung Surveyor's Gaide^ 
And likewire ihrnugh c, and d, and where- 
thefe Lines Interfe^ giiret, you. the very 
corner ar j : Next from the point C, priclc 
off 2 c.%Ci I. and at right Anglei to the point 
at 2 c. jo/, prick off i c. 20 /. to the Hed^ 
at g, and draw the black Line g f : N«xt 
from the point C : prick off 3 c. 9a /. and 
at that diflance prick off* i c 40 f at right 
Argues, to the Hedge at h, and dratv the. 
Black-line h g,then tram the point C prick of£ 
& c. 30 /. to die Station at D j at this S-a-. 
tion D prick off So Links to- the H^dge at 
c, and ;o Links to k, both at right Anglesc 
At the Station D prick the Qiiantity of the 
Angle CDE with ypur protractor, whirfc 
(ontains n%' 30' then from the point D, 
Viih yotir Scale prick cfF ^c. 60I. and at 
r'^ht Angles to this Mark lad fet off, prick. 
oti I c ^° It to the Angle at C, and draw 
the Lines Ik and h i, till the; inteiffO. 
each other, which will give^ou rfie corner 
(itz.,At the Station.D, Pnckoff^Sc. 15,/^- 
from yout Scale of tqual p9ri8,and at right 
Angles to this laft Mark prick off i c. 50 /. 
to the Angle at m; and draw the Black- 
line m I. Ar the Station D, prick, off' upon 
the Line DE 1 3,f. 20 I. to the Station at Ej 
fromthis S.atron priib off jo Jj^riks at 
eight A^gka tp.the Hedge at n^acd 30 Lin. 
to-.the Hedgft at 05 at the, point E protraft 
the Quantify of ,(he Angle DEE with your 
grotrai^or , which contains $i9>' '. o''ihen 
. ' ' * fronk. 



The Toung Swveyor's Guide. 1S5 
frf4n the point E prick off 4c 10 /. where 
at louchfs the Hedge at p, then prick off 
&€. 30 /. to your Station at F. prick off ai 
the point F yo L'nks at right Ang'es to 
the corner at g, ihen draw the Blatk-Jines 
pq po. Likewiiedraw the Biack-iincs m n- 
where (he two X^ines m n and p o Interfeft 
^ives -you the very cotner of the Field at 
y: at the point F, prottafit the Quantity of 
the /Ingle EFA with your protraftor, which 
contains loS" 3kj, and if the Line FA falls 
in (he point A-, year work is rfg'it fo far: 
From the point F prick off 2 c. 70 /. from 
which pcanr prick off at r%tit Angles 85 
■Links 'o the Atigle at s ; then from the 
^oini F priik off 6 c. 6')t. and if 6 c. 6^1, 
tench s jbfl to the poiTj' A,ycu msy be aflu:- 
ed your Survey was taken truly, To enclofe 
your Field draw the Blaik-line from q to 
8. and from b to a, the line c b and f a be- 
ing contintifd, will intefftct at w, the very 
corner which enclofea your Field, 

N. B. As I have reroniinended io ihii 
iiiample the thin Ruler with t-qual 'partj, 
upon iJie very Edge to protrfia with , be* 
ing mjjch better than Compaffes on 
many Accounts, as every fi-jrveyor will 
' find. So I wouM adwfe every S'lrvpyor, 
that is curious, to make ufe of Mr If^jrdi 
Proiraftor improved : The Semi-Circle is 
inade near as ufual jupon thij Semi-Circle ii 
jnoveabl* Index of 7 Inches lorg,theuppec 
put 



iS<5 The Tbung Surveyor's Gm3e* ■ 
part bfing ; degrees from the Center, and- 
the lower psrt next the Limb } 4 Degrees, fb 
that pach E<4ge wit] be Diagnnal of ooe deg. 
\-tipoa this. Edge '^ unequal Pivifioos Caicu- 
) laced to every Minnie. This DefcriptioD is 
''' -accordirg to Mr Warir^ inftead ot having 
the Index thiis made, I think it much better 
>to have that part of the Index above the 
tAcnb to be part of aa Arch of two degrees, 
and th« other part fu^pofed to pafs thro' 
th^Centre:Now upon this Index thfDIvifiant 
will be fqual, and will be conliderably - 
larger at the beginning of the DiviHons ihaa 
ID the other. The D^oionflration oT this de>- 
pends uponTfco. 1 3 where 'tis proved that the 
Argle at the Center is double to that at the 
Ctrcutnferenoe. The ufe ot thii Inftruimat it 
very eafy i for you hava no more to do 
' but to let the Index to the whole dfg'ee« 
obferved, and upon the Ind^x graduated, 
prick off the Minutes; This Protraaor 
with Srales, ai before mentioned, ' with all 
forts of Mathematioil InftdJments,are made 
and (old by Benjamht Scot ( who fervid f)h 
timi with Mr Rowley,) he keeps a Shopai 
the Miriner and GJt^e over againft fxrtfr 
Cbavge in the Strand. 

Having now recommended proper Inftrii- 
ments for protradling your Olifetvatioits, 

{cannot avoid acquanting the Reader, that 
he heft Inftrament to take Angles, is the 
Theoda- 






,..&„, .1, 



Tlse Toung Sttrviyor*s Guide, 1 6y 

XheoJoUie with Teleftope fights, as every 

'Pra<^ioiKr will foon find the Advantage % as 

fcst the plain Table, it is a proper InHru-' 

ment for Learners of this Art to ufe it fof 

a Imall Inclofure or two, fuch ai Gardens, 

or GroBtid-pIots of HjoOs, fSfc. But 'tis a 

Ihame for any Auill to ufe this Inftra- 

rqeni tp Survey a GentleiiianB Efiate.",! 

have Surveyed ^fl'e^thofe who have ufed this 

lDl1rumen[,aiid I have increafed upon him no 

lefs ihao^wo Acriei io. afield of 20. This 

' was occ^oned by his going out in. fuch a 

Morning diat was Fof g/, which -dampt his 

Paper, and after he had workt about two 

- Huuri the Sun ftion?, out and diminifhed 

I \m plot upn his plain Table to the above- 

i fnentioneii nf o Aqfes. Tha like Eftor ha» 

i been cortimittcd by ihe Circum%encor, 

^ 1 hope Gentlemen and others will take thisin- 

- to their Confidera'ion, and not fufFer them- 

felves to be impof?^ upon Yiy having fuch 

-' Inftrumentsufed in Surveying their Eftates. 

The Dividing (or runing off) both Ri^bt lined 
I and IrrtguUr Figure's^ into 91 many partt u 

you fi-tU M^nir', ^<pii'l or mequal. 

\ . P R B L E M I 

\ To cut off from a Triangle any parts, 

« ttr* ^'- ^'^l* » ^^^ ifluing from any 
^nglc afligned. _ 

.1 



i68 The Touf^ Surveyor*^ Guith, 

R U t P.. 

XriaDgUi canfiftirg.oF equalBifes^ani 
and in .rhe -fame Pariillel are ^qual ^ there- 
fore take 7, f , t» Cf- of the Line oppofife 
Whe Angle \ draw a Linf, urtiich fliall \n- 
nde. a TBangte. to.tontaiB the paiu re- 

j^ig.ics. Admit ABC, tote a Triangle^ 
whoie. ^ part is required to be cat off, 
with a Line iffiiing cnt of tlie Angle B, to 
cat the Line AC j and then wiH Afi be ;one 
fide of the Triangk : Tden' let rfit i part 
of the Triangles Bafe be taken, wliidi endeth 
in D, and let the Line BD be drawn, whirii 
iiicludelh rhe Triangle ABD, which is the 
^ part ef the Triangle ABt. 

PS Q B L^ M n. 

To cat off from a Triangle any number ^ 
of MeafureB, . as-^, B, 8, 3a, G'c with a 
Line iflliing out of the Argle afllgned. 

R D I E. 

iFlrft Meafure the Area of the whole Tfi- 

«ilgle, then multiply the fide pppofitp f«- 

tht 



TheToung Surveyor*! Gmde, 16^ 
'th« Argle afligned1>y rhe parts to be cut ol^ 
and divide the [»odu£l hytkt Pttea of the 
wTi^e Triangle ^ the Qootient Diewi how 
much you Oiall cat of^ to make a TcJangU 
to coDlain (he required. 

Bxamffle, 

Figi 102. 1-et ABC b« a Tiiang> giveti^ 
and let the PropoHtion be to cut ^ S4 

rti, with a Line ifluing from the A^gU 
and falling on the Line AC, and malf 
tog Be one of the fide« of the new Xri» 
ang^e ; fiifl, the whole content of the 
Tfiai^leABC* it found to be 3;^ Hav- 
ing proceeded (I'iub, let 84 be di6 Ntmera>- 
tor, and 336 fhe Denominator, wbich being 
aUireviated thas, it< , -rrr. tt. t "rf the 
Contem ; rhrn proceed in all Tefpedi as yon 
did in the lad Problem, and you Aiall i^nd 
the Triangle BCD, to contain 84. parts of 
the Area « tht Triangle. AfiC» which wa« 
leguind. 

r Jritbmeticatly "performed. 

Firft, The CoiHenfot Ann of the wholt 
Triangle ABC, being^out)d to contain iT;6^ 
and ih< Line AC 42.} then fay by the 
Rule of PrqjioKion, asdie whole Area^?^, 
isto4a) foiB tbeleiTerArea 84, loafourth 
Nuaiber, which is found 10 4. io the lame 
1 Pawlle;, 



] 70 The Tormg Surveyor's Gmde* 
Parallel, which fet from C tourards A^ wbidi 
falleth ID D: then draw the Liae BD, 
which Triangle BCD, confains 84 gan8,.the 
thing required. 

P RO B LB M III. 

To cut off any number of parts, as 20, 
40. 60, fc. in a Trianglf, Propertional 
to the Triangle gtven^, with a Line ^ral- 
leJ to anjr fide given. 

R U L E, 

ftrfi, Meafure the whole Triangle, then 
Square any of (he fides, in which jou ' 
would have fhe Parallel to cut 1 ihatS^aie 
number multiply by the parts giwn to be 
cut off, and divide the ptodu& by the 
Area of the whole Figur^j out of which 
Quotient eitraa the SqaitrRoot, and it 
Ihews how much yoa ihall take of the fide 
of the Triangle, to make a new TriaOgle j 
with which Meafure found, fct ttfim B 
to G. 

Exam^ 

Fig. 103 . Let ABC be a Trianglt si«b, 

from which 112 ia to be cut <wF with a 

Line Parallel to the Xinc CAj the Tfi- 

jiiigle being Qieafured, and found to be ^^6^ 

then 



The Tow^- St/Beyer's Guide, 471 
Aen put 113 over for tbe Numerator, 3i]d 
3j6 ander it (or-theDrtiOminator; anil by 
abbreviatiag.it, you Ihall find the fame, to 
te t, th*n having deft^bed ihs Semi-Circle 
on the Vne AB, divide iheUne AB 'into 
.3 equal parts, and from arte of them ere£t 
tte Perpendicn'ar DE ; then taJw the Jiftarica 
from B to E, and fet (lie fame from B, to^ 
wards A,.which endeth in. F; by wliicK 
poim draw a Line Paratlel to AC : S3 
ihs Triple BGF doth contain 112,. m 
was required. ' , . 

^ jirh^metieal^ peffprpted.' "- | 

■*B!^^ Square the'lMe BC'io, WWtfiihate^ 
400 i then fay, as ^6 is to 490, the Square 
of that fide, fe is 1 12 to t;^ f, wfcofe Square 
Root ifl Tif near rational j which is the df- 

,. flimce from B to G i fb a Line dratfn from. 

! 13 ■ Patallet to CA, you h^t the Trfaugl*. 
BGF, ,which contains irs, as before. ': .. 



>ff oj: n jH IV. 



From a Triangle gtrei^ to lay tJie parti 
-cut t^ in » Traperiant i if there 6e a Pro- 
portion given between the parts cut ^ 
and the whole Figure., 

;. - . ! 



V 

173 The Tmng Surveyor* i Guide, 

i^^. 104. Let the Triargle ABCbegiveD» 
from whence y is to be cut off in a Tra- 
ptzium : Firlt then on the Line CB defcribe 
a S>;mi-Circle i rhen divide CB into 5 equal 
rarts, and of 3 of ibein from B, ered the 

* Perpendicular DE, then felting' pne Foot at 
your CompafieBiB B,<irend the other to E, 
-which diftance fer off from B lowardi C, 
which endtth in F^ bj which point draw 
% Line Parallel to AC: So I include the Tii- 
angle GF^ to coniain .^ of the whole : 

. And confegueiKly th'e Trapezium ACF6 
doib coBtain T of ^kefamrai was required. 

Fitfl taV 4- froip the whole, the remainc'er ' 
-will be'4-5 then by the laft Problem make 
tSe iTiiangle GFB to contain ^, and 'heo 
it will follow, that the Trapezium ACFG 
mufl contain ^ of the whole Tiiangle^which 
was required. 



vi ■ 



PROS llEM y. 



''To' dividea Triangle, when the Lme 
of Partition goes not parallel with any iide, 
take ttuG iiiimple. 



TlEw Toung Surveyor's Guide, 705 

T'^ to^.Let ABC be a Triangle to bs 
divided into two larts which ftiall bear 
Proportion to one another, as ? and z, by a 
Line drawn fromihe point D in the Bi& 
or Line AC. 

From the limited point draw a Line 
to the Angle B j then divide the Bafe AC 
into five equal parts, and from the 'third 
point of Division draw the L*ne to E, Pa- 
ratlel to BO. Lctfiij, from £ draw the Line 
ED, fo fliall the Xnpfzium ABED be in 
CoiHent as three to two, to the new Tri- 
angle DEC. 

I have now done with the D'.vifTon of Tri- 
angles, when I have added thefe thre* 
Advectifemenrs. 

- Firft^ Yob ■ mnft be fute to lake very er- 
i&Iy.thc di&ance of evei^.Foinr, wlur» a 
dividing Line cutteth any flde, -to one of 
the ends of. the fi'me fide, as in the Uft 
Figare, thcj diAance BE and AD, which di- 
flances beii^g applied to the Scale by which' 
the Figure was protra£):ed with, will fheyr 
^ at how many CKaihs and Links end, yniv 
are to maks your dividing Line on thr 
Field itfelf. 

Second^ The proportions by which yom 
are to divide, are not always fo formaily 
given as in the former -Example, but ar^- 
wmetime to be f(Hind out by Arithmetical' 
working, as in this Cile. 

I I Suppofer 



JE74 "^^^ Toung Siirvsyor*s Guide. 

Sappore a Trui^letof 6 Acrt«, 2 RMids, 
^i Perches, mufl be divided, fo as ibe one 
of ihe.2 paitsihall bs'^ Acnes ; Roods, 
- oad ^ Perchct, tnd the odier oon&quentlj 
I Acre, 5 Roods, and 26 Peiches; reduc* 
liotli meafnA's into Perchea,tnd the one will 
be 765, 3Dd!the other ^06. There Sum il 
1C7I; which by their common meafuie be- 
ing reduced itiro their loweft tf rms of Fra- 
portion in whole nnmbers,wi)l be 5, 2, and 
7, which {hews that the Triangle being di- 
vided in 7 fgual parts, tbe one moft havc- 
5 of fhofe 7 parts, and the other s. And 
nb&ire that it nrili be fafHcient to find 
ihecomrasn jneafbre between the Sam of 
rhe Terms, and either of the Terms % the 
Method whereof is Diewed in every Arith- 
roatical Book for reducing Frmaioiis into 
th«ir lowefl Tenni. 

Tbirdy In thefe and all other Divifioos.oF 
l,aiid, wiiete a ftrii^ Proportion td Qiun* 
tiry is to b* obrerped, yon muft have re- 
fpt& toriieJtules hereafter delivered. Bat 
if there be Tiny ofeful Pond or Well try 
draw the Line of Divifion ttiroagh ; hw if 
there be anunufeful Pond, Lake or Paddlei 
or ii there be any Boggy or barren Ground, 
that muft be catlout in the Divi&n ; mea- 
fure that firft, and fubftfaft it from the Con- 
tent of tbe whole Clofe, and then fay the 
juft Quantity of the remaiiider on tbar fide 
that is^lxee fiomit, th« the other may have 
fait 



TW Vowtg Surveyof^s XhuJe. 175 
his jofl p«t alfo, beftdes that 'which is 
nfelefi. ' 

PRO B I EM< VI. 

To cut ofiT from a Square vaj part pro* 
pouoded in a Parallelogram. 

RULE, 

Divide the parts (n be cut off, by the fide 
■ef' the Square % the Qiiotient fbews hour much 
of the fide of the Square you (hall take for - 
the Bifadth of the i?^rallelogram ; at which 
diilaoce draw s Parallel Line 5 which QuU 
include the ParaUelograiD re^nted* 

ExamfJe, 

3^i. 106. Admit ABCDtobe a Sgiiarc gj- 
¥«», whofe iide is 20; from whence 160 
parrs is to be cat olf with a Line Paralltl 
10 CD, fo then CD makes one of the fidfa 

(rf the Panllelogiam-, then work as is he- 
)ore taught, and draw the Line EF? which 
i}iclud£[h the Parallelogram CD£F, and 
contains li^o, the parts rfaiired. 

iVtrte, And if yon would have CHt off -',, 
■^,£^c.. then yog (puft divide the SquartSide 
to be cut off into thefe Pioporriooal parts, 
^d.^by thofe pait3,draw a Parallel Line, 
which wouU. have included a Parallelo* 
I 4 gram- 



17^ Tbe-Toung Sim}eyor''i^ CmJe* 
gram to have contained the part* Propo»- 
taonable. 

FRO n LE M TO; 

From an Imgalar Figure to cut off any^ 
parfi repaired. 

RULE: 

Meafure fo ntany f riarglea Ijirig next 
to the part affigned, rili you have fomething; 
too nnich, then by the firft and fecond 
Problem of this part, cut of the overpluft 
from the laft T'iangle, foftiU you haTe tk 
figure to contain the parts rtqaired, • 

J^g. 1 07. Admit ABCDEFG to be a Plof, 
from whence 480 parts are to be cut ofT 
with a Line ifliiing trom C, wd to be re- 
wards the fide AB : Firft, let the Trape* 
»um ABCG be mnfured^whofe Area is 370; 
which added to 1 7.6, the Area ol the Tn- 
aFgle CFG malceth $.06, which is too much 
by 26, which 26 let be cot off from the 
Triangle CFG, by the Line C b ; fe doth the 
F:gnre ABC b G , contain 480, the parts re- 
quired to be cut off 

Note, This Problem is very rnaterial i» 

the Ffad^ce of Surveying, in dividing and 

IpyiBg; 



Tl&ff Taung Surveyor's Gui3e, 177 
i^jring oat Groundi, whether into parts 
cqaal or uneqiial % which every Sorveyot 
ought wtll to acquaint himfelf with. 

For the better anderflanding this pointy 
we will fuppofe a point given in the Peri- 
meter of the Plot, from which the faid Plot 
is to be divided ioto as many eqnal parts* 
as fhall be requited t F»ft, Mtafure the- 
Area of the wholfe Plrt^,~then divide that" 
Content hy the number of parts (0 be cat: 
off, and' the Qijotientihewethhow many 
meafures each part Ihall contain } them 
rut o£E each paTt Teverally, as^yoamre: 
tau^t in the preceedjng worfc^ ^ 

P RO-B L EM Vm« 

To divide a Cotnmoo-Field or FHObR;. 
into as many parti as Diall be retailed ^ 
according to each ISaa^t Vso^xaoa. ot 
RfcDt: 

ExampUf I^ 

1^, ro8: £et ABCB£BGH£]r bta, 
Common-Field or Failure, ia the Ufe- audi 
Occupation of three Men, vis^ A,^C,.and! 
it is agreed by them all,, that each Mas Oialb 
have nts Staportion of- Gtaund hid ouf;, 
according,to hia-Qjiantitj^ol Common ji^ 
tb*. fanft i^cr^ 



17B The Tintng &trve^'^ GiMefe^ 

Firfi^ Meafore the wtiole FicI;], add iC 
will lie fouqd to contain 3; j^.;U. 1; P. 
'>i' 7735 Perches i ihcnconfider Iww many 
B^afe-Garec lher« are in th^ Paflure, and di- 
yide the Q.uantif/ of th* field accofdingly 
hy the rule of Proporrion, rhus j faying, if 
tne whole number of BeaGi-Gat;! of A,B> C 

five ihe' ivliole C^a^tity of Perdies in the 
ield $7;5^ wjitit flia^ the ivimbcr of them 
htloogiag to A, be, and the Anfver will 
lie his part( and fi> work (ererally for each 
Mans part : Bgt we may fuppofe them tbus^ 
•©■A,»8i7 Perches, to B, i7i6Perdiea, to 
C,i202 Perches. Then to lay a\fi tvay 
Mans Fiot, 1 divide the Figure by the Di* 
felons afgrrgoing h-j t^ Lioeii B L,and 
CMy which to lay out upon the' Grouad, 
take- livmybLH'Scalethetli^nceoDthef lot . 
brtween H and L, th«n meafiire out iks di~ 
fimoe on the Qiouiid from the Aogle^ £i 
to L, atfo from the Angle A, Meafure oiff 
^v^\6 to B, then draw the Line BLj sr 
gain take from TOUT Scfk the duantlty of 
XM 28. 00, which meaiure on the GrounJ^^ 
from L rp M, anfl there fet a Mark ;. and 
an like ' manner M«afure frpm B to C upoi^ 
Che G;oBnd 25,^ 10, e,quA]l fo B^ UQon th9 
pW, dn3wiQg |he;l4i^ 04^ So u yoqr 
^ot divid^-.a^fiQiding: ti^«v«y Mansjufi 
.<C^aiiUiJ; an4; ^ofortujOt 



lUeT^Kg Suivgjfor^s GitiJe, 179. 

Example II. 

' Fig. io(). But fuppofe it W3I required to di* 
vide thip Field between three Ferfons, viz. 
A,B,C, according to eachMass proportion of 
Reyt I As fuppof^ the whole Grounds to b^ 
so FcNjnds 9 Year, whereof A pays 9 /. B7 L 
C4i' the Quezon is, . how many Acres, 
Roods and Perthes belong to each. Man^ 
aKt:ordiiig to his Proportion of Rent, which 
by tJie Rule of three argue thus^ ( fffifor 
ji)lt 20I the whole Rent, give 573 y 
Perches,^ (btitg the Contmt of the vbvle Fieli 
in PercbeSj) what wjU ^'1. ^ive? w/z, 2581 
Parchea,. or 16 A o R. 21 P. beiflg the pro- 
portion of Ground beloiiging to A, for his 
9 /. Rent. In like manner, & will have 1 z 
A. z R. 07 Parches, being his Quantity of 
Ground proportionable to hi^ent of 7/, and" 
Cfor hi< 4/. )<jeat,^will have 7At,oH 37 
Perdiss. 7hen to lay out theCe pacts upon> 
the Groimd, oh&tV4 th« dizedwiu in, th^ 
dinner Example^ 

PROB I^b'm I3L 

- To diwide » Field into three equal jrarrt-, 
jBid e«cb Man to have the Begt^ of a Pbnct 
about the middle of the Field. 

Suppofe J;]g.i £0. containing' 27Acres i»tn &r 

diiCdedbetweeathtee Men^ e|<di (o have 9 

iBcrc* 



off The Toung Surveyor's Gm4h^ 
Acres, and the Lines of Pivifion to ruot 
from a Pood in the Field» To that every 
one n^ay hare the Ben^t of ^e Water, 
wi'hoiK going over anoihers L-iod, 

Firft from the pond ® draw ILines to 
•very Anglei ® A, © B o C, ® D, © E, 
ind then la the Fjgnre divided into j Tri^ 
anglct each of which meafure, and put the 
Contents feretaliy ^ which Content* n^ct; 
4}1 into Pctchei fo will the Triargle,. 



Eercbei^ 



Tlie whole Content hieing 4340 Per^ 
^eaor 27 Acres, each Mans Propartion 
oeiiig 1.44,0. Frnm ® to any Angle draw 
a Liof foE the firft divifion Line as O A.. 
X^eu cortiider. that the fii$ Xtiai^le A ® ' 
% is bu' 6?4 E^rches and the fecood B O C. 
3?c^ both together but 1064 Parches, lefshy- 
376 than- 1-440, one Mans Portion : Yoa ■ 
miiS-thtreforeoit o£P.from the third Angle- 
C: D 376 Perches for the firftMan'i Divid-- 
ing line j which thn» you may do t The 
Bale I^C is t% Chaioaii the Gonitsnt sf tbe- 




The T^mig Surveyor^ Gmdk i84 
Triangle 1238 Perches: Say then, if 1299 
Perches give 18 Chains, 00 Links, what 
(hall 57? Perches give ^ Anfver^ 5 Chain* 
4$ Links i which^ fet from C to F, and" 
drawing ihe Line F, 700 have the fiift 
Al^ni part, v'rz.. A ® F. 

&em^/^,See what remains of theTrianglci 
C D 376 being taken out, and you will 
£nd it (o be 862 P*rche», which-is lefi by 
578 than 1440., Therefore from the Tn^ 
angle D O E cut off 578 Perches^ and the 
point of D'.vidon will fall in G. Draw the 
5,fne G,, which with A and © F di-^ 
vides the Figure into tiiree equal parw^ 

rR B t E M X: 

To make a Parallelt>gram having an> 
Angle equal ro any Angle given j and a; 
fide of any Bergth, which ftiall be equal' 
to Ihe Area ol any Right-lined Figure- 
whatfoever. 

K^.in.Le* ABCDE rtprerent a Fiel J* 
of 5 jJOequal SidfS,. andit-was rfq ired to^• 
lay out a Parallelogtam that fliall contairt 
the fame Area, draw the priekt Lines E BR 
and DB, then have ybu nMd« th» field to 
confift ot three Tlianglw. Make the Tri- 
angle a b e equal to the TliaPgU A^¥. by 
Fnb. & Btvtde the Bai^ eb Inio two e- 
quaL partt at Z;, and draw- the Line a z^^ 
«iluctL dindtt the Xnan^ e a b into two 



1^3 The Tomg^rv/yor*j Guitff. 
tqual pacts, vlx.. th; Tnafigle eaz ;;;: to- 

the Triangle abz {hytbeerem i c^ at the pouit 
9 make the Aogle n s b ~ to the Angle F. 
draw n in Parallel to zb, and of equal 
t<eogth to 2 b, drav m b Parallel to n z 
and of f^ual Length to n z, then is the 
Parallelograiji m n z b (iqual to the Xriat^Ie 
cab. N^w becaufeit isrtq.jited thatap-aral- 
lelogram ihould hare its i)de equal to thrline 
A B, continue the Linen m, and make m x 
cqal to AB.cotitinue (h<Linezb^Dd uiake-br 
eqqal to m x, aad }oin, the Line x r^ from the 
point xand b, draw the prjckt Line at plea-* 
&re,'coptinue the. Lii)c o z to i^tiirfiA at 
the point o, draw oy Parallel tozr, and 
continue the Line m b to UDterfe^ at p; 
making p'y equal and Parallel to b r, and 
join the Line r y; then it the P'.trailelogrtm' 
bry p, ei}ual to tne Parallelogram n m b z, 
by Theorem 1 1. In like nranner make 
t|ie F.traUeIogr^m py.q S filial to the Tri- 
angle EBD-i likewift make the parallelo- 
gram s q * h equal to the Triangle DBC,(hea 
)vin the EaraUeic^ram b r f hbe rqual to the 
Jtight-line Figure ABCDE Q.EF and QED. 
If it w<re require^ 10 lay out. a Rlght- 
^gled Faral1elcg[am . fqqal to the fame, 
I^i^t-liqed ' Figure, aod ^e.Side fgual to^ - 
the Liiw. AB, let the Right-lijied Figure 
ABCDE contain 12 Acres ^ adding 5 Gjp- 
phers t(y it, the fame Field willcontain 
xj^oooo S^te Links ; X^t th; Liae AB le- 
grcfeol 



TBe T^ag Surveyor's ^'urdih i^^ 
prefent the Length of a Hedge given con- 
taining 6q Chains 0% 6090 Links ■, Divide 
1 200000 by 6000 aod Ae Qaotient will 
be 2000 Liokp or 20 Chains for ihe Breadib 
of the Right-Ahgled Riralklograoii foe 
200a Links multiplyed by 60*10 Linki, 
produces 1^200000 Square Links, or t^ 
Sqaaxt Acres^ 

2b reduce Stattat-meaptre4o Cufiomarj-imafwe^ 
and toe Contrary. 

Although an Acre of Land by Statute i»- 
to contain 160 Square Parches, of i^ feet 
and # in the Perch ; yet in fome places of 
the Nation, throngh Jong Giiftom, there 
is at this day other prrcheg ufed, as 18,, 
20, 24, and 28 Feet to the Perch y it i» 
therefore neceflary to fliew hnw to teducfr 
Sratutemeature to Cuftoinary, Cc. 

Suppofe therefore you would reduce 
Statute meaftre to Wxiod-land-meaferi of 
18 Fe^ to the Pfrch, then 'fey, 

M the Square ot the greater perch of 18- 
Feet, is to the Square of^the leflfcr Pt:rch of 
rS Feet aod i i fo is thf Content in Acres, 
accojding to th« hSkt Perchj to the Coiv 
tent in Acres ^ ^cco(ding to the gcestec 



7 



^4 7^ Tmmg Surveyor*^! Gai^g. 

Let it therefore be required' to redtice ^6 
Acres, 2 Roods, lo Perchei, at r^ Feet and 
4- to the Pferch,. into Wood-hnd-meafare of 
l3 Feet to the Perch. 

F'lrJI, Tou mud obfeive (hat the Sgoare 
of .16 Feet and \ is Dechnally 272, ay^ 
and the Square of 18 Feet is 324 ; then I 
reduce the 36 Acrn 2 Roodi, lo Perches^ 
into Perches, which makes 585^, rfieh I 
multiply the fame hy tlie Square of the 
lefftr P^rch, 272. 25, and the Produft i» 
r;92662. ;o, being divided by the Square 
of the greater Perch. 524, the QnotientJi 
491 y, "3 25, which is 30 Acres, 2 Roods, 2j: 
Perches for tlic Jtfwer^ 

Btit fuppofe you would' reduce Wood-^ 
land-meafure into 9 atate-meafure, then fay^. 

As the Square of the lefler Perch of t6^ 
Feet and 4-, is to the S^are of the greater 
pitch r.8 Feet -, fo is the Content in Acres, 
according (o.the greater Perch to the Comeok 
inAcresi according to the lefler. Perch. 

.^MC ta CJfJjl vp tfc CiAttetftofany flaty im 
Jern^ Roodi^ mi Bercha. 

H/. ii2i Admit the ft^owing Figtn«> 

noted with the E^etters A^^B, C, D, E, I^^ 

G^H, 4 ^ tb&plotof. B Field, whofe 

CoJttenti 



The y^mng S««wj«ar/ Guide* i9% 
CcHitent in Acra, Roods and Pcrdus is- 
Rqaired. 

Fi,fi, Then ( in aU fmh Cafes ) dirida 
7oar Plot info Trapezia's and Triangles ;, 
accordingly (his figore ift diifided into 
one Trapezium, as K, D, P. I, and four 
Triangles ; for finding theArea of all urhich^ 
begin with any one nrR, and multiply tlw 
wniDle of the Bafe by cne half of ine Ptf- 
pendicular , or {which » alms) (he wliole 
«f the PerpendicuW, by the \ of the Bafe j. 
the produd either of the Content of that 
Triangle;, and then Som op all the Area's 
of the &vsral Triangles to<u:iheE, gives yau. 
tha Cont«iU of die whole Elot. 

t^S^STk. )T"«i. D £ F 1-3-00 
Triangles be. ^^^.^^ ^^p ^J^^^^^ 

The, Ace»d(th« W^ole Field. 1 2 --2— oi: 



Sut the nuA exa0 way of all, i« to 
moln'ply the Lei^rh of the Bafe of each- 
Triangle, ■ by the Length of the Perpendi- 
cnlar ^ the Strni Total of alt the Trianglea 
being' halved, gives the true Area>of the 
whpli! Field in 8^are Link*, (or Chmi^mi 



1 8tf " Th« ToungSwve^s Guide. 
Lhih^ which may be redocid it lafl ih 
thefomer DireSmt) into Acres, Uxoie ud 
"PtiKka. 

Of la^^ imt KetfZtmi:, 

A certain Qointity of Aorct being giren, 
flow to lay om the £tnK in a Square 

figure. 

RULE 

Asnez to ^Iie DBmber of Aceri given 
fire Cyphers, which will tum ihe Acrfs 
into L^nks.^ than from the Kun^ier tbui 
increafed, eztmft the Square Root, which 
fiiall' be the ficje of the propofed Sqoare, 

-^ - . Eium^U. "■.,■". 

Sappole the Kmnber ^iveo to he loo 
.Acres, which J am to Jay in a Square Fi- 
eace } Z join -to the-too, five Cyphers, and 
&en it U looooQoo SftiR^ .Lttks , the 
Reetef which is 31^2 neareA, or 3t Thuins 
62 Links the Lergth of one fide of the 
■Square. 

Again, If I wen tocot otitof aCoTB- 
'Field one Square A;ae,i 1 sdd tooaefi^ 
jCyphera, and then itj<jooooo, <he Root 
■of whidi is.i^ Chaiaa \6 Jbinln , antf 
iCboBthing more,, lof the Cdeof Ithe AcT^^'.. 



The.Th^ Survejt^^s Guided . 1-87 

Uavte Uy out atrif given ^uwtky of Acres 
« « PunpffsJigrwo, whereof one fidt it 



R XT t E. 

Turn firfi ^f Aa» into Links, t>7 ad- 
^ioig ai befoise fii'e Ciphers 5 rfiar Nnmber 
thus increafed,iUFide by the given Sidf^thr 
Quotieat will be the other Side. 

Example; 

Let it be rfguired to by out too 
Acres in a Parallelo^ni , one iide o£ 
nvbich (faall te 2a Chains : F'aQ to the 1 00 
A<yes I add five Cyphers, and it is 100^ 
130000 , whid^ ( divide by 20 Chains^ the 
Quotient is 50. Chains, -for the other fide of 
the Parallelogram. 

How to make a Triangle that fhall con* 
tain any number of Acres, being confined 
tcia certain Baff^ 

B V L S. 

Doable die given number of Acres, t» 
which annex fivtCypherSjWhich divide by the 
Biie } the Quotient will be the Length ot the 
^pendiculas. Tbisnecdano £aaaplr. 



I 8 8 TJ» TUmg Surveyor'* Guidt. 

Horn tty find the i^a^cf^t l^jmeter of *■ 
Circle:, vbich fiaU cancan cmj liai^er »f 
Jeret, 

u tr I E. 

S37, as iinrto 14, fo will the Number of 
Acrei given , be ta the Square of ibe V^t- 
saetet of the Circle required. 

Example^ ■ 

XVhat*« (he Length, of the Diameter of 9 
Circle, whofe iup*rficial Content (hall be 
Joo Acrei > Add five Cyphers to; the loo, 
and it makes too 00000 Links, which 
multiply by 14. it makes r'40000CQO j 
whirh divide by n, gives for the Qjuotient 
12727272 ) the Root of which is 3; Chain*, 
6-j and fomewhat more And fo much Ihall 
he the Diameter of the required Circle^ 

How to reduce a large Plot of Laoi 
ar Map into a lefler Comp^fs, according to 
•ny given Propoition \ £?" tfoirtr, how to 
anlarge if. 

Ftg. iis-TShe befl way to do thi»> is-, if 
your plot be not too large, to Plot if over 
ag^ by a finaller Scale ) but if it be large. 



The ToUng Surveyor's Guide. 189 
as the "Mx^ of a County, or the like, the 
only way is to compafs io the Plot fitk 
within one Sijuare, and aftetwatds to divide 
that into as oiany little Squaret, as you 
fiiall fee convenient. Alfo make the fame 
number of little Squares up<Hl a Fair piece 
t>f Paper, by a leiler Scale, accordiqg to the 
'Proportion given. Tlui done, fre ia what 
; Square, and part of (he fame Square, any 
reuurkable Accident happens to fall, and 
BOTordingly put it down in the leiTer 
Squares $ and that you may not mifbke, 
it ii a good way to numbet your Squares. 
I cannot make it plainer then by giving 
you the following Example, where the'Plot 
ABCD, made by a Scaled to Chaini ia 
ao Inch, ii reduced into the Plot EFGH, U 
30 Chains in an Inch. 

What has been hitherto laid concerning 
reducirgof. a Plot Hxata a greater to a 
IffTer Volumn, the fame is to be under- 
flood vice vetftf of enlarging a Plot from 
. a It^Ter to a ^eater. But this feldom comei 
in Pfadice. 

Knowing the Content of a piece of Ltnd, 
to find oat what Scale it was plotted by. 
4 Fir^, By any Scale meafurc the Content 
of the plot } which done, the Proportion is 
as the. Content found, is to the. Square of 
the Scale it was tried by ; fo is the Content, 
to the Square of the uue Scale it was plotted 
by, 

Examglfi 



• 90 Th Toung Smrveyor's Guide, 

Admit, ttiere is a ^ax of a jnece cf ]|uid 
-containing 10 Acres, and I meafure it by 
a^caJe of 1 1 in an loch, find it contain 
12 /teres. 

Then I fay; if 12 gires for its Scale i^j. 
What fliall 10 gire> 

Mfver^ 10. Therefore I conclade jt wai 
Allotted vf a Scale of lo in an loch, ' 



^ I -N ^ S, 



APPENDI.X. 






the Totmg S^wgor's Guide, i ^i 



Ion? to take the Gremdffjot : 
^ofahy dty or Corpbramn 
; bytbtTheodolkeorDegreer _ 
■ on the plane Table. 



FOR (he potfOTimince of wjiith, Jt^ill.; 
be neceffary foF th« ^oung, fiijHvey«r to ' 
provide himfilr of a Cheutt thatis: Je'f'oot 
long, contiioing ;o Lmks, and esch Vaik s 
Foofi foB all Ciijes are befl Iwd dotvn by 

H Scale of Feet: It will be convenient . tbat 
he bawi b Rbd that is 5 'J^' Jo Fopt: In.' 
Lc[igth,and tolie fDbdivKli!d-ipto.F4et;'3:his 
Rod is ti&tate the ^DSf^ofthtiHotifM OS/ 

r borti 5de8 your Clniii, aa.youmeaifiirealaag ; 

;'the^»eet»orIjiaefi. ^ 



■93 ITx Tmmg Surveyor* s GuiSe, 

Exampla, 

iji !Rg. ^. ht i part-of (braeCitj, and 
yoa are ivquiretl to t^ a {jroQtKt-plot 
thereof. 

FiHl, Caufe two Men to ftand, one A 
B, -Hd tbectber at- F ^ tittfi .facing yoqr 
laftironeof at A, Iayihg'tlie*Iiid«z ,v^ 
ttk Dntmetei:, torrf it ^btsuMmtil ttvoogh 
the S-^ts you efpif the Man at ¥ ; thea 
fcrew your Inftrument faft, and direiEt your 
Sights to the Man at B, and note the .degreei 
cot b^ the Index, which let be 9; deg. and 
30 lAm. Not« this 9; deg, and 30 oiitk 
down in your Field- Book,' as yon did when 
Titu ineafnred the Lane-, then with your 
Rod nipafure yoer Off feti both the Right 
and l«ft, a$ yoa did in meafuriog the Lane 
alfo ■, which yoa will find to be to the RigTtt 
5 Feet t then with your Chiin meafure to^ 
wards 8, and at ^ Foot difiance froin A, 
TOO will have yoar Off-fet to the Lefr (o 
M 7 Feft; 'Tibte botfa thefe down in your 
Feld-Book orEy&d taught, which is beft tore- 

refent the thing 1 theruneaTuring on rou!»d 
you will find that at 47'Feet didance 
from A, you «il1 have a Street both to the 
Right and Lefr^abd the Oft-fetTo the Right, 
will be 10 Foot, and to the L^ 6 y note: 
thefe down in your Field Book or Eye- 
draugftt i then ftill miafurtag toward B, 
you 



Tht Toung Stmieym-'i Guide. 193 
you will find ihat at 90 Foot diftance 
from A, yoB wiil haffe an Off-fet to the 
Left that IS 5 Foot \ note thia down in your 
V eld Book, alid at the fame time yoof 
Off (e« to the Right •'ill *e 1 1 Foot j note 
' Hiis doifrftalfo i then come to B, where one 
of yoOT Men Sood, and by ipearutlrg with 
your ©lain, you will fiD^the diftante be* 
llten A and B to be voo Foot i then pla- 
ins your Inflfliment ?t B (cauTmg the Mm 
that «bii(*rF, <o flsfid at A, lo fonn as 
you tot^ your Inftiument up from A ) 
htyilig your Index upon the Diameter, *unt 
your Inftrumenr abotii until yju through 
ifc'Sighn i:fj?y the Man»t Ai there maka 
Wtmi InftKiHieM ftft. anj'caule theMan 
filal flood at B, to go and (land at C , thea 
afr^a your SisllH to C, and note the deg. 
cnt by thelndel, wtiich let be 140 deg. then 
withyour Rod'meafurethe Off-fel both to 
(he Right and Left, and you will find that to 
(heRidit is 1 1 Foot, and to the Left 8 Footi 
their ^Mfe your Men to meafure towards 
C, 1h as direa a Line as they cm, and at 
61 Foot diflance from B, you haveaStreea 
both to the Right and Left i then meaTiire 
the Offfets, and you will find it will ba 
a Foot on both fides the way, vis. to the 
Right and Left, at 120 Foot dilbnce from 
B, the OfFfet to the Left willbe found ta 
be 8 Foot, and at 127 Fool difbnce from 
B the Off fet to the right i< 8 Foot alfo , 
K thep 



194 TbeToung Smi}ey9r^s.0Hi<k- 
tlifn youwiU find you jnbc^M^tflQi tbcp 
table a ftfonrogoindfand tit<@« j^c^an- 
oibttto ft»iul«tDv plvx 3r4of ?#^nnii 
atC, and fay ithe rintkzltaereof «BpBMlif 
•Diitiiietflr^Ttuinirg it abviit.'tiUl^pifgti th^ 
Si^hrs you-cTpifc ttie'MBtfatBi:tfta<if(^*V 
■yourbmruqiar/afi ^ theh dii^^ 71041 Stehcf 
■to ibe Man « D, .abd/tfw tn^ltiE wilf-l)^ 
found to cut ttoo-degj and^if.you/inea^ufi 
wiifa yon Kod.. the Offr^flp.tbfiTiglu.j^ 
(he 'wiie tiint, ittirilL'be.fcmiid^rfd %f^^ 
.'Foot^t then ineifiire ttith yi6ur;;Oi|ait:^ to* 
wards D, and at gFootdi^n^^ ^em C^ 
the OfT-fet to the left will be foqfid.'lp'be'p 
Foot; then jnesTuK on . w^Ji; yjif^ piui^ 
and you will fibd that at ^4' j^g^f^l^piis 
framQ ttM0fffettoth«dercis4fFaat^'||f 



iS4rt'a«tfra 



75 Foot the.diftanc£>of QS, 
the right it .12'Fcut ii.tbea^piacF.i^iml 
flniment at D, and catrie a Afa^i to^pa^ffa^ 
C, anri another at £^ and lE^'ipg^tneJqd^ 
of the laflrunientiipoo ^ .Piap^af;.,, jmip 
it aixiut till tbfough.'ihe Sifi^ -3^ ^U^ 
the Man at G t, thettwak^ f(m.}^^mitn^ 
iaft; then diretfl your ^ghMagw^ W§tM 
ark\and you wiWrfuid that th« ^dex.V^tqit' 
icodeg-ihen withyonrRodjineafiire thtutf. 
fet to t1ie tight, and it.itfiU be iqurid ^ b|| ^ , 
Foot,and tiileOfF-ict to the-)«ft,ii ;Foot ^fi^tf 
wiill 7tnti:<^1^in' ineafrKe; tourardt^i^.jttiff 
at 4T Foot aiflance from D y.o".wJI^^ l^a^^ 
a Strett-td.t he right and , lafr 5 4fc^ nia^u^ 
itig on cewatdi £, .you will ^nd that at 



■ The Tbung Sttrveyor*s Guide. 195 
•'91' iFoBt'diflatice"ftotn D-yoU mflKai'e An 

Gff'fet'ia'ftdl^iefrt^iif-jFoor andthewhola 
'd!H»n<(« b^lwe^^^D and E will 'be found 
' td %fc ic<3''F£K?t','t!ifen^ladng Vcur Inftfti- 
' flt'E, caufe «' Man \o ftand at I), and an- 

tJther ar F, and lay the Indej upon the 
■'Diameter, -and-tarnyoap Instilment 'alnjiit 
'■flB'yfeu'-ef^ie the Man it D' j ,t1if re nlat« 
■'faftj-Dorlnft^unifrrf/ana'direiayobP Sight* 
' tojF'^driote (he dtgrci-'scat Ijythe^fn- 
?deijtvhifch'^«?ifl '!« found to 'be a r'b deje- 
■iheii *ffith youi'Rod mpafure rUe Offlfct to 
'the R%ht, apd jt wiM be foitnd*' to be, 7 
. Foot i tTiiefl with yonr Chain inVaffif e A- 
^v^fds Fi^ aUd at! 9 Foot d-rftafnce fii)to E, 

■imil I-«f( j W(^Mei;ar^tb^ (ifaWifafeT^I 
'lie"Fbilnd to ht to the RikHf: 7 T^obr, sllnl 
■ to 'the- Left 12 Fooci flrl^ Afsl%tn^ (b- 
. wards ti fm'lViW 'ffiid that w '-70<^o$i'^. 
-flance firpiit P;' yoiir lift'Satftrf, 'Jdni Will 
-fifl* tbe-Offilt to tht''t.d/t'w'be'7¥6of, 
■anfffe CMfftt.tb'tKe %?ic;ii.W ^F6r* 
-^the Whfclti.^iftance betw^eeriE^j64''f h'f r 
Foot, then flacftig ybi]i::''inftftiriKhe'at F, 
caufe a Man to ■Kand ' aV A, and anoihartj* 
flahd At E>''ihe"iflace ufhere, yon J?R harflfc 
-9rttion,--thetf'T3^^ ■yout.liides iipon tH« 
Ojamtter of yofal''llillriiiiiehr,.toin the'-ftriia 
abt«\tuntil.rtirpughM SlgliW'ylju eCpie tlltt 
'MajJat'EV 'th^-c make ybur Inftrmnent 
'ftftj aocf dJreti Voar Sights' to ttw Man 
- ■ li» «« 



if6 The Teamg Surv^r*s Guide, 

that ftandi it A, ard 70a wilt ^od the- In- 

dfZ will cut 74 deg. and 30 iniit,thai whh 

your Chain DKafure (owaids A, and at S 

Foot diflaoce Tiom F the OS-^k to il|e 

Right will be found to be -5 Foot, and to 

-the Left 7 Foot \ then nieafuting. on to- 

-watda A, at 67 Foot diAance fiom F, yoa 

will have a 5<ceet,both to' (be Right and 

..J^eTt } jind Hill mtafurirg 00 towards A,M 

1 123 Foot diftance from F, the OfT^fet to 

-the Right is 4 Foot, and to the L-ft J 

, Foor, and the whole diftance between F and 

Ji. is 129 Foot, then have yon done with 

.^e Obfeivaiions in the Hign Streeti. 

Nftfy Vou are to fet down all your 
' Ohfervaiions at yoiigo along in yoor Ficld- 
' £aok or Eyc'draugbt, which is beil. You 
may make an Eye>draughr thui^ Firft go 
along the place that you intend to take a 
Tlot of, and draw Lines to imitate the fame, 
-with (fors Sireetsif there be any, noting 
your Sratioos therein by (his Maik ^, ; fet- 
line at every Station the Angles oblerved, 
:ana the Off-fet oh either £de the. X-"nc, as 
you find it to be when you take theiii,andthe 
'jLngthoI the Lines betwf«n Station and 
£iation,and ly this means when youcame to 
^protrad your Woik, you will have a leprt- 
.ftntatioii of all the Work that you have 
,takrn i but if yoB fet down aU your Ob- 
liervaiionsin your Field B^ok, it will be Uf- 
>eflary to£etthein4owiiiii auBDeruul forjn 



Thf Toung Survefor*s Ginide. t^y- 

nfTtbU^ObfenutmttMktawbmjniiwtiit abtut the 
'High Streeti. , 



■ot-& 


S»Oi"H 


A(to.|DI/l.l 


X. 


X. 

00 




i m.l Ftii. ' 


SI 


1®4 


JS 30 




■s 


at- 




6 from A 


00 


7 


«— 




47 from A 






i-f — 




— 'i Street R.*L: 


10 


<9 


•t— 




« from A 





5 


'•■: 




"o from A 


\1 


00 


3eB 


140 60I00 (from A- 


n 


8 


at— 




''■feomBaSfireet 
iotheR:&l. 










9 


9 


■«r- 


, 


"ofeooiB 


.0 


8 


;»t- 




■^TjftomB 


■'.8 


00 


a.ec 


Kut <K 


>»W*onrB: 


8 


<?o 


,at- 




f4- 


Froni C ■ ' 


00 


9 


at— 


00 o< 


fromC 


00 


4 


at— 




7? 


from C ■ 


12 


00 


4«'C 


100 00 


7! 


fromC. 


9 


II 


at— 




41 


frornDsSffft 
'0 the ,R. » L 












■ J cot 


,at— 


• ■' ■ 


91 


From R ' 


CO 


7 


J«E 


2tO 00 


roo 


From D 






at— 




9 


aStreetR.&L. 


] 


12 


at— 




i: 


from E ' 


7 


< aF 


H t° 


fromE 


; 




»t- 




8 


rom'F 




7 ■ 


at— 




«7 


iStreet R. ItL 






at- 


00.00 


.n 


PromF 


4 


T 








K] 




uviog 



198 1 7Tfeit^> SWrt«^f GWiift.' 

Ha^ifJg'thttsrtkeil j^oiir High Streets, ym 
m m ill the like mimieiJpttce^ widi ttw o- 
thef fm^l Streets and LincBi. with feveral 
Boug^ and Breaches, noting doftntifymrtj 
Ej,e*4raijefit^f^l''i' 1* Booiagaiuft evtiy one 1 
of thfin, Ifhe'OffreTsTq the RigTit dr Ldt, 
according; as yoy 6ad<hamon either fid« | 
of; yoqr dhain. ,. - ; - ^.. ■ p :< ' 

^o/e, 1 1!^'}9 tfnhei^.yhii. t^e yoot| omw 
Sft^'et^itwill b9Cpn;v«Di«Ki8often ^»yM ' 
-cdm^ iijgp^ftany^^Sireeftotakc ^Sigbt . 
dditfn iy, iand no'te^he't^bce oc tpatk t)^t ' 
yifu ti^keJo, and tJift,pl2csdf fiandingwhra , 
ydfi uke yoHi Sij^ht to ;fi>y Mark thsA is la 
tht ao!^ Srreets ui jour Eye-dnughB wilh | 
thUMvkj0, andfq^by <h«einean< yqtiWfi] I 
know wh4ce to p|tc« y^tiriaffaanent'^^biil 
r^u'&fl^to take, ^ecroTs Streets-,; your | 
li^h Streets and; your cipfE Stt'Dis being ; 
trai^ t^en, in th« next place you are ^otake . 
the .tntafure of the Houtes to the Froat;<and i 
lit^ifc t^e deptfaf o^.every oneof the^and '■ 
wjth jrou^ Red. or' feetfil talje the Ptott of • 
yqur Coutts and A%ys, fiifl 5y drawuigttn ' 
Eyc-drau^ of tJ^m, fetting- upotf et*/ 
Break or Retuni.tfiereof the meafure you 
took with your Rod % and id fo doing, you 
will find ifnoharj matter To protia£t die 
Tame after {you havjp fMtjiiftet^ both fides of 
*very Street ^ /or you wjll;haTe the ReiffC- 
. -fentation of ever^ Couft ^ad; Alfey [n lt& 
proper pl^. ' ' 



II 



CHAP. 



F 



i .-.'; i!.:!l ; rll,M-l ;ii.')ii',(!j . 1 . 
jKioi^n i:r" J H V. Ill'; . )1 {•\'. ;■ . 

.srav- 'if. -' >^"a iw- '■■■'■ ■■■'--; 

Hmd tavUttiMa HoK.i'Uy dom> my 
\'^;qblir^t0fM¥tkmding to the 

K,) .iil.I 5:i: ,;:■!, .'.;,■ , ;; 

>IHIj hii*itie-"prtlnded'yodr<elf of .good 

t'TjM tt :la(glk| t«ii«utAr« tte Liu 

f^())H^iWl(i[)oWlltt'{li)llU,[i<ara TantPl^- 
rfMtor ftmiiiH)! liKW«rAaiha>«iln 
^t!^>cUtl»fintt'AP'^' dun'&ding byi 
3*«u^Fi«U>II(Mc 01 Ej'e-dniBbt tkat th* 
An^l^eKctVMtur'A, vit.^i Org, and 30 
il>ii<j'«^t ^'ti^ fo arin. •( ytiut Pio> 
tfkWI^■ltlft•'«'Mi•Ujl»nddiltal the Liu 
A'^.lrf W^il!; oHn. fiildit^g.Biro Hnn lh« 
']aiBthitfiA3>-^aa't)ba'ftot^ nilea icoirotn 
off yfbrBoAe pf iqtnl Parts, . and place it 
fnnbA'toB^ then plaoiDg the Cenrer of 
your. Pr^airidsr. on ine-Jsoinc B,- torn ycuf 
enmriaiir Ibodt tlnUI thoCin^ A£ therAjiC 
laJinSl^iqlOil Hirlait A b hfidrawn , 
Ibfa-' Aiding 'that: tha Angle, obieived at B 
ttw'-^'^adeg-'«gaiBft'l4eof yoof Pcouadof 
make a Nbuk with y6ot pcolra^iqg .pin^ 
K 4 ~ and 



300 The Tou^g Swveyor's GuiiU* 
and draw the Line B C at Itngth ; then find- 
ing atfo that the length <^ B C was 1 27 foot, 
(axe 1 37 from off yonr Scale of equal ^vtb, 
and place it from B to C j. then ujring the 
Center of your Protni^tor upbn the point C, 
turn it about until the Line A B thereof lie 
dirrdtly on the Line BCUftdriwot thni. 
iuiding by your Fleld-BoolE or Eye;di;aD|bt 
tfiatihe Angle obierved at Cwas ioodeg.a* 
gainft 100 de'g. ^with your pH>tiaffing*pin 
make a Mar}^ and draw the Line C Dal 
Irngth i then Ending that the iHigth of the. 
Line waa 7!> foot, take 7; foot firotn off yoor 
Scale of equal part»» and ptBC« it fxom C ta; 
D ; then lay the Ceftter of yota Prptraao> 
uponD, and torn it about qotil die Live A 
b thereof lie dircaiy oil the Line D C laA 
^awn i then finding by your Field-Book or 
l^ye-draughi that at D you did obferve an 
Angle of 100 deg. therefore againfl 100 deg* 
of youf J^otiaaor, iriib your prcttrafiing-^ 
pa make iJOixt, and dnv the Line D^ 
at lei^ V then finding aUo ^ttlM InogtV 
of your Line D E wai too fbbt, take looi' 
from off yoor Scale of equal parts, andplace 
it frpm D to £ { theii remove your Pn>tra6tor, 
and lay the Center tbercof: upon the point E, 
and finding by yonr Field-Boolk the Angle 
obferved at £ was 310 dcg. agaxnfl'iiode^' 
of yonr Protra^r tiiake a Mark with yoat^ 
protrafUng-pin,' and draw the Liiie 0^«al 
length i then finding that the length of £F nraa 
83 



The Toung ^atje/or's Guide, aoi 
83 foot^ :take 8j from off yom Scale of e- 
qual pdrtt, and place it from £ to F ^ then 
placing the Center of yout Proirador upon 
the point F, turn it about nntil the Line AB 
thereof lie diredly on the Line EF lift drawn; 
then finding by your Field-Book that the 
Angle obferrsd at F was 74. deg. and 30 
nin.,againft the fame d^. and min.of year 
Frotra^r m»ke a Mark with yonr protrad4 
iog-pin, and draw the Line F Aj which it 
you have protraded right, will tall to fas 
cza^ly 129 foot; then have yoa [tcotnfieil 
yotir priocipil Lines. Kow bcgifi to pro^ 
oad yoar Off-fets thus. 
: jFir/, finding by your ^U Bookor Eye- 
dfaogfarthat at your firft flation A, the Off* 
frt to the Right was 7 foot, take $ foot from 
off your Scale of equal parte, and plsoe it 
fromAtoa-, then finding alfo that at 6 fint- 
diftaace from A, the Ofi^fet to the Left wa»- 
7 foot, take 7 foot from off the faiae Snle. 
of equal pvts, diat ycm protnficd-yovr' 
principil Linn trom, andpfaiM it-froia jL^ 
loo ^tben finding that at 47 foot diflance 
from A, the Off fet to ih« Right was to 
foot, iake 10 from off yoar Se^«f e^al! 
pvtt, md plare it fioan « on the Line AB« ■ 
to 2; asd draw the Lrae a sat lengths . 
ibcn finding alfo. at the^fime timetiw 0£h - 
let to the Left »u 6 fool, take fr^em off ^ ' 
your Scale, and fettin^^one pcrini ot 
your Cempaflec Jn^»^ on the Line AB^- 
vith. the other jnake a Mark on the' Left 
K 5 , baa : 



los . IhiTaiHg Surveyor's Gttide, 
fund of t^e Lise. A B, and dl'sw a Lioe 
froJn 9 tb rhifl r laft l/imk 'made ^ . ithen br* 
erafeyoli find by- ^ur Field- Book ihac aft 
t&e Jal} Dffftfts dmre wis a Sunt both to 
ths-Rishtaod Lert^ yofx muftmakc a Mark 
^■fignirjr^hefaiiie^i then findiag by your 
Fiel^BM^ thai at- 9{z foot ilillanec itoOi A«. 
the OiNetto Ihctcft trai $ fDDt,lb«[t;$&oa 
tafceHfl;fraiiioff7«T:JScAleof«^lpafts»and 
ftniag «ne//cbt of ^r Cmripaues in-rhs 
piinC /, with the'othw tna3ce s fmati MarJr 
to*^ Ldt tMnd: af the'Line \AB, and 
itXK^A Luv froiil the >SlKit toi ihis Maric^ 
the Offfet to the B^kt atthBTarmej fim 
waffliQ-iiiiff:^ 't^S 'thtt -I's fdot. firdm ^oiF 
7^btJr'S<3i]<t Bt]d^feltiigi:oiie.foot of 3rotir 
€&ailM<]>ffmthe,pDiDt; with ths olth«t tmkA 
d'Msr^ on the R^t fid« of the Line :AB, 
diȣdrilw a Line Aram the Street itirthia 
MvkiUS «riad« -, ifi^'Bifdif% itet vbyoot 
«ki8n!i»;i'yed1iaa> ifae£)ff&t:i«*he.]tiehe 
!fr-^t)->fisk!»:q[rA^inioff'^o«r< Seale^ of 

.-paflcf' i^ tiiei p&^l^ B; .wah theoiher^ ma^ 
«'Maf4p oiftfiS ftigbP-hana-iTde 6f thk Line 
£G4^Hf 6lili6tw thefanu timeitothe lit^ 
VM «i':aorv) «ikt i&^fbot fraiq loff ^yuw 
ScaU of equtl ^^ana^and fitRibg.' aae Jose 
c^'^eQr6«ttipai&£aintlKpdiflt£, WJihthfr 
liMiemiddct a:Maik'0h the: Left Iid4 of 'the 
KinfBe'i then folding by yom PieM-Baolt; 
or £j«-^augfit that -at 6i foot, theOf^ 
// ,:i i.; : ..:: .: : ..-■; ■.■.., um 



«tt(^tlte m^ apd Left vac 9 fooT, tske 
^irQcntCj^OW^cale of equal parts, and 
^tring^ one foot ol your CompaiTes in the 
point p, with the other m^e a Mark on 
both fideathe Line ^ then draurLinet on both 
fidei of the X^ioc BC, Uom the Mac^ made 
on. both fidei of the Line at3, to ihe Marks 
Ia$ made \ and becaufe there is- a'Street «• 
the Offfei lafl taken, make a Mark to 
lignify the fame at 1 20 foot diftance j&om 
b, the Offfet to ihe Left was 8 foot j taka 
8. from off youf Scale ot equal parn^ 
anifetting o|k foot ot ]ra«c Conip»fr<4 is 
the point V, with- the other make a Maik> 
on the lAi fide of the l^nt B C ^ and draw 
a Liflfl from th« Street on the left fide of the 
Liae BC to the laft Mark Qiade ^ then a| 
yourfUtion C, you bad an OSTet to ther^ 
Ki^t of 8 , foot^lfo ) take 8 Tioin oS yoor 
Sealepf equ^ 'pactt, and rating dds foot 
of; jTRur Cam^uOlei ialhe pnin« C, with the 
othnr nntlEfe ,« Muk^oa the Righ^ iide of ths 
Lint Be, and draw . a Liae from the Mark, 
tlial you mada forthtStte^ oathe Right 
fid« vC the LiM BC, through the latt Mark. 
madeat Ungih % then fuidiii)} by yotirFieU* 
'Sfoak M Kye^nneht, that when yoo had 
db£«re4itlM^&0gW'a« 0, yo^ had an Oif-fet 
•o^beiRisbtaf a foot, tak« 3 foot from o£f. • 
yotv Scale of rqal parts, and fettiog one ' 
ipot. (^jfow .Compares in the point C^ 
with Ok drtwi ) «»b I « iM M ^ ftjfhi.. 



ao4 The Tomg Surveyor's Guide. 
fide of th» Line CD I you likewife imd >t 
8 foot diftance from C, yoa had an Off>(et 
10 the L"ft of y foot i therefore rake ^^com 
your Scale of equal parti , and plating ope 
foot of your Compafles in the point X, with 
the oth«r make a Mark on the Left fide of 
the Line C D ) yoa will Hkewife find by 
your FieH-Bookor Eye-drarghtth5rar ^4 
foot diflance from C, yon had art OSktto 
the Left 4 foot » take 4 from oft' your Scale 
of f q'lal parts, and fetting one foot of your 
Compaflea in the point Z, with the other 
make a Mark on the Left £de of the Line 
CO, and draw a Line from the Mark that 
was made oc the Left fide of theUne CD, 
at X, to the inark laft madei then by your 
Field-Book y 00 will find that at your ftg- 
rion D, the Off-fet to (he Right was 1 2 foot j, 
lake 1 2 foot from off your Stale, and fel- 
ling one fcot of your Compaflesin the poinl 
D, with the other make a Mark on the R^t 
fide of the Line CD, and draw « Line from 
the Mark that was made on the right fide of 
the Line CD, vis. at C to the Mark latt 
madej thf n findirg that whffi yon obfeived 
yruf ^rgleatD, you had the Off-fet ta 
the Righr 9 foot, and to the Left 11 foot, 
take 9 foot from off youc Scale of equal 
p^rts, and placing one foot of your Com-- 
pafTes in the point D, with the ether main 
a Mark on the rrght fide of the Line D£^ 
and take 11 from eff the fime Scale, &t> 
ting 

„,.,,.„..Coc»;lc 



TheTtmngSwwyoT^s Guide, aoy 
ting Mie foot as before in O, make a M»k 
on the kft Jide of the Line £>E with the' 
other { by your Field-Book you-will find 
that at 41 foot diftance Irom D you had a 
Street both to the Right and Left ^ make a 
Mark to figntfy the fame : Likewife yen 
will by yfinr F.ifId-B>ok i]iid that at 513 
fiiol diflance from D, you had au Off-iet to 
the Right of $ foot i take 5 trom off youf 
Scale of equal parts, and fetting one lootttf 
your Compares ia the point Y, with ^ o> 
ther make a Maik on the right fide of the 
Line E^, and.diuw aline horn the Mark 
nude at D, v on the rig^t ^de of the Lint 
DE, fo tbe Mark lafl irade at length, until 
it doih'iat^rfe^ the Line that was drawn on 
(he right fide of the Line CO: Yoe. witt 
find by your Field-Bookthat at yonrStatioa 
E,.the Offfet to the Left was 7 foot) thi» 
7 foot tike from off your Scilt ol tgiial parts^ 
and fetting one fobt of your CompaiT^s in 
the point E, inth tbe oihrr make aMaik on. 
the left fide of the line DE, and draw a 
Line from the M»k made on the UU fide 
of the Line Dti, at D « to this Mark Jaft 
drawn at length ; yr>a will find by your 
Field'Book that at 9 foot diAaeee from E 
towards F, you had as Ofl-lVt to the Right. 
y foot, and to the Lft liioot^ ihrretore 
take 7 foot from yt-ur Scale of fqual part% 
and luting one foot cf your GompsjTs in 
Ibe poim H, with lbs ouux oak* aMaijc 



oD thi righi ifide ijS the Lide F£ ; andMin* 
wjfr take 1 2 from the fame Scale,, and : p)a- 
dng one foot- of ytut Cdinpii^s as b<iare, 
in the point H, with the other make a Maik 
on the left Hde of the Line iF, *nd draw a 
Line framthe Msrlc that wai made oq tbt. 
left fide fif the Line DC, at IT^ to tbis' 
Mark laft 'laade } iheu becaufe thefe two )aft 
Off-&ti wsrev the Coiners of tWo Stcceu, 
itukc a Mark to fignify the fame } at 70 fool 
dfffautc* from E towards F, the OR- fet to 
the Right was 7 fjot, and to the L-ft 7 
&ot'alio, take 7 footifrom oif jrour.Scate.oi 
equal jaitts, and placing one fool of yvat. 
0)mp»ires ill the pant K,' with theothdr; 
make a Mark on earh £de rl the Lin^ EF,' 
and draw a Line frokn the Mark that w« 
made on the right iide df- the Line EF. tit 
H, to the Mark that was laft made on the 
p^kt'^e ef the'LiihejEPat Ki} ^Bd diaw.a 
Lmc likewife'ff dm the Mark ihatwu made.- 
au the left iide of fhe LoierEF, at H, to 
the Maik that wasi laft jhade oti the Irfr fide 
of the Line EF, at K ; then by your Field- 
Bbok you will' find that at y^r Station F, 
foot' Off-fit to ttie Right was 5 hot ; take- 
^'from year Srale of equal parts, anid pk^ 
Cibg'-one fdat tif yBarCompafTts in-.the: 
point F,' with the othei make a Msik oir 
the rigHt iide -of the Line FA, and at 8 fool 
diftance frnm F, you had al^ tbeOfF-fet i», 
the Lflt 7 £e>M ) taJse 7 fmmoQ-ytnir^ak. 
■^■■^ of 



of f!(pisltp4Kl^>iaBd'<pItcaigiqn«foOTof^ur 
Compaffi«^a the foinr N, with the other 
make iMirfc-6n the I/sft fi.de tjf (he Lid* 
F A. At 67 Foot diflance from F, you had 
i &ieet to the Right and Ltft ^ therefort 
makeaMarkto Hgnifie the fame} at iz^' 
foot diftance (mm F, towards A (by ytnif 
Field-Book you will find) .you had an Ofi- 
fitt to the Right 4' f6ot i take 4. from oS 
you^ Scale of etjQal parts, and plu:tng oda 
foot of your Compadf s in the point R, with 
{he other make a .Mark on ^e right iide 
ef'tic^Line FA, anddrawa Line from the 
i/bfii that was; made on tbe right fide of tfab 
liine FA, at thrpoiat K, tothe pomtthair 
^shft- made,, fo that tbe Line whidi yad 
dravr may ioterQd the Line which isidrawn 
(HI the light £de of .the Line £F, and: tbs' 
I^ine that ii ^rawn on the right iide of the 
line AB^ tJien at tiieTame timeyoahsd: 
M OlB&ttatbeLeft,-, of 5 foot ; take ifl 
likewife fronk yducSc^eo^ equal parts, and! 
friacing onfe' root ofyooe GoeapaiSfit in tQ£ 
Boiot R,withlhe oe^ipt inake-a Mark on the: 
Lft fide of th«LifteFA,ard drava Linefromr 
^e Mark tJiat was mtdeoDth^kllfid^Dptht^ 
lJinEFA,BiNjto tbt Mark thiittarailBft made* 
«n3hs;left iide of ^fadKLnibatiRv t^Koh^yft: 
Tou mnd^ a> end of protiafiiagi^loub HigH- 
Streets : in the (ame manner, you muR pro^ 
traa your fcry-Lanea and Streetp. llda niuft' 
likewife deal fb. witb all AUejsthat lata. 
Tbocoiigh farea. ^[ow 



ao8 The Toimg Survejf^ Oai^g. 

Ynut Street! and Lan«t being ttnis pro- 
traded, 70U may proceed to theprorrading 
and laying down the Groand-plot nf the fe- 
Teral Hcufes thereon ^ for the doing ot which, 
it will be ronTenient that you have a finalt 
Scale that is adiially divided into 50 equal 
parrs in an Inch ; then laying your Scale 
a long by the iide of the Line e, and 
againA the meadred breadth of each 
Houfe, with yoor protrading pin make a 
Mark or Marks } then lay the Edge of your 
fmall Scale along the iide oi the Line e S, 
and againft the meafureof eadi federal Hou& 
that ii thereon, with yoar protraAing-pin 
make a Mark -, then lay jour fmall Scale a- 
long the fide of the line SQ, and finding 
by your Eye-Draught that there is a Coart 
oc Yard, fiifl make a Mark againft the 
meafare ofthe Teveral Hoofei until you con» 
ta the: Court or Yard, and then mark oottbe 
bfeadthofiheEnrranrc thereof as you did (he 
breadth of the Honlrs^ and likewife maka 
Mifks agaitift the breadth of each Hoaleon 
the other iide of iheCourt alfo ^ then laying 
yoat finall Ruler or Scale -along the fide of 
the Line Q.O, againfl the mufure of the 
breadth of each feveral Hotife, wrthyour pro* 
trading pin make a Mark. Having thus laid 
down the breadth of eacbfeveiil Houfe,. ib* 
next thing yon do lay down the depth of 
each Hosfe, and draw Lines- in the famt 
inaaaer as jfou &t thofe ia tbe i^ and 
. -, fludour 



The Toung Survejors Guide* 109 
Aiadow ihetn alfo aa you fee , that thejp 
may reprefent the Gtound-plat of. a Houfe. 
. ■ When you come to protraft (he Courtj 
lay your Eyc-drau^t before you. Mid draw 
(he beiidtng and turning according to difcK- 
tion, laying down the mcafure or each fevt' 
ral Houfe that is therein, as you did in iha 
Streets {..you tpuft-alfo protradt the Yard^ 
6r Gardeus'that are t^hind the Houff s ^ with 
the turnings and windingt thereof accord^ 
ioely as you lake them. 

Mjte^ That when you lalce ibe Groorid* 
plot of any( hurch, youmuft be very exai^ 
in raking the ButtrelT^s, and the Steepis, 
^demy one of the Palais, and protract 
or lay tfieai down in t^ fame foim and mea* 
Cire as you found ihetn I^jnding, and |ha^ 
dour them very deep , that they may b4 
known to be Churches. 

You mull , Itkewife ufe the like txs&ntlt 
in meafuring and protia^ing HjJIi, Tnns of 
Court, Celledget, an4',aU eminent Hoiifett 
and Ihadow jdum acceidin^ly. . , 






2IO The Toung Survey's GukJe. 



^■■^ ^ Comtries^ - sK jdr^e^ TraSi 
■'of Land. 



tE 



(reared gf Un^ftier^) alr'^arfy 'i' arid ttlflfe* 
/farii, W^pbrtng rtJaf' ihe Ingeijious Sarvejror 
cannofbe incapable of ^pnlying it tJ tfiil 
fri*rft*cil/dr^ IftUl: tfholty omit this, arfrf 

Leai'iltfrwyfhemaiidiniMr ^^ori'ftmiMf 
phioij. 'in' oViiet !tb' wh/cfa, 1^ ''lis ^fenil^ 
the fblfbwtiig Lenimata. ' ' '- ' ' ' "' ;' ' 
-I. AH faundG are pitipagated almqfl even- 
ly,' and are obferved to move 8 nifafur«d 
Miltfsjo 37 Secohd*; '' '.' ' '. ' 

'•'Thfirfe tvell 'kiwwD 'ffom,tWla(^,1iM 
moft accurate (5bfervatfori(iafcQOT'''^~*"' ' ■ " 
Ihe Velocity of Sounds, which */*'^»-7'r'* 
arethpfeof Mr^rn-iflM. * *^- 

11. An ordinary Mortar is eafily able to 
caft a Projcfiile about a Mile in Perpendi- 
^lar Heigih; and the Sound thfreof maj 
Be heard near 20 Miles. 

The troth of both ihefe Propofitions have 
been fufBcIently proved by divers Experi- 
meoti made by Mr Wbifion iat, that purpofe. 



The Toang Sarve^*^ Guide, ' ' all 
III. A. Projeaiie may '6b fiU'd with 
Con^ufiibld Matters^: to xAb Fidc ai fi>ont 
as difcba^'d^!: ^d icDndnqe hmtiiDg itiUt 
it comestQ-fltt.GrtJuijd.' ■ ■ \\'.r. .■ [i i^ 

Tbii ^11: that 'deaS. innRockett, Bomb(r»' 
and Mortflra, do vnyMeW Knbur, and k 
found~ to be due npon Tryal. 

. lyj'Firr,' orLiglic abontis billc higtrl 

will:i' bt \rifiJ?t'iil'»he-JJIrght': ihae, *hen« 

the AsT ii tolrrab^xidai abodr,7ta 'Miles* >0 

This alfo harh bee n made tn anifeft 1^ 

many iRpkrTnwnU ihade on puipoTit i 

' Tir&I^'iw ofthe,PrMem. ■■■_ 

Let it jShelL^I^ wil^ali e Fite^ fi»D «i 

difchii^^, ' aid Jconttnae ^itfnifi ^ill it 
comes to 'rfrt Grqund/be ftot'j*! sCndicil- 
larly at)op^ a Mtle higlfi otK pf a Mortar al 
any conrrmcnt place in' a -clear Night j 
and this Diicharge will by th» 3eaif DSi *^^ 
Interval of t^e Fla^ and Boian^; gi?g the 
DiRance and ^Besritrg of an O^^.r^tr'tcithin 
the Hearing ^iid Sight .thereof; affording to 
the foregoing Lemmata. ' -. 

. - Example ^ ' '.^ : 

F^g. -A.-' t.ft 'rhe^Beaiiog oF'ISh^ dif-. 
charg'd oat of a Mortar at C, and alfo the 
Inrlrval'iof Ibe fM-«nf SaMtt thereof be 

obfuv^d ■■ bf r^tSala^6iA to' wA E)K>'0;i 
H.I.D. 



313 The Toung Surveyor's Guide. 
H;I.D. placn within 30 Miles nmnd C, who 
muft be fumiOird with an InflninKnt ta' 
mtafure Angleti f(»r taking the Bearing of 
the fhell i and a Thread 39,2 Inches long, 
with s Plummet fafien'd' to one end, which 
being fufpended by the other end to a Pin,or 
Kail, and made to fwing, will vilMvte feconda 
by which (he Inferral betwem the Ftafh and 
Sound may be nicely meafuied, and let thtir 
Ot&ivatioos be aa foUova. 



i 

1 


I'll 


■ ■§' 


lit- 


'fe-. 


14 1 




Is*'? 






Miles. 


D. 


a i . 


s.e: n 


14 


A. 


.,'74 


1? 


16 


e., 


5St 


12 


E. 


835- 


S.\ir.4o 


iS 


F. 


Jl 


90 


11 ' 


I. 


J!t 


N.E. 5 


12 


H 


78 r 


. !o 


17 


S 


«9.± 


aW.Sa 


, '! - 



Tftpmtraa which , trough tfct' 
fam C, i)t>« tin Ucitdno N. S. and lay 

off 



The Toung ^irveyor's Guidi, 3 1 j 
cfftheAngl«iNCD.3',NCA. 5o%NCG. 
-^7',(romlheNonhtowardsihe Weft. Thf 
AngtesNCE^o°,NCF.£>o\(rom theNorth to- 
wards thellaft.Tbe Angles SCI. «'^CH 50*', 
liom (he South towards the Weft, Laph 
Lay off the Angle SCB 6o'' from thfc 
South.towards ihe Eaft. Then fet off their 
^tflanai ftom (h« Mortar 3t C m%. DG -=. 
-i4»i, A C — 16 m. iS'c. actordiflg to the 
•Obfervaiions. So will you have an eiafl 
Map of ihe place A.aC.UE.'F.G.H.L, and 
Ihe ScitiMttion of the Villages about each 
Station tn^y be eafily taken by the Oi^rvec 
there.0f after the common method td takiiw 
onacainble Diftancea. 

COkkOL^RTt. . 

t U each Obferver were to let off a 
Rocket at his own Sration, and rdk« the 
mutual Beartog, of eafh others it woud be a 

freat Check to any Error that could pofli- 
ly happen. 

II. If a great Gun were difcharg'd near 
Ihe Mortar, and the Sound ttweof uied in- 
ftr'ad of that of theMortar^ it would be beard 
much further, and cooTequefUlr a mndi- 
larger Traa of Land might be torreyed at 
once. 






•14 72v Tonne Survgyor^j GuiJu 

A teaij vaj to fnd a trte MeridiattUne hy \hf 
PeltSur. ■ . 

The rigbt Afoenfion of the Pole Star fqi 

this Year (171^ '• ?7 Minutes of Tioiej' 
-and it increafes sne Minute 16 Secondiere- 

Sten Years : Therefore having at any timt 
is Stir's Right Afcc^Mi; and the Ri^- 
'A&ennon t)f the Sun both in TtnW, if 70a 
firi^rad thelM(# ffom the^onAer,- adding 
54 Hours to the Right Afcfenfion of the 
. i'ule-Star, ■ «1ien it iff left than the Sun's 
{he Rcmaindervrillbethe rime of the $ftif\ 
coming to the Meridian^ at-whidi time 
hang tip two Pendulums between your Eye 
and the Pqlet'lSbiv -iiid a Right*htie drawn 
through them, will be. a true Meridian- 
iirie^ •! 1 :■•■'■. ■■ ;' ■ ' , 

in the Snrvey jufl now treated of,' yoa 
aiiay nfe ihe -fighh of -a good CircumfereD- 
tor, loi^aop MhsrSHrre^inglnftiaihrtit,' ha- 
ving one of the fights long ■ enobgh ta 
lake inf*iPblefltar: ''' ':':■! ■ 
■ ' If you ■ wt«*d kmfr, what -'Angle the 
£oie*Star mak&s' with the' true Meridian ^ 
atiwbertimw, the fallowing Table will J 
ibdr- -:■... :-■.'. ...y. i . •" 



Sideral 



Coo^ik \ 



' The Toung Survefor's Gniie. i rj 



merlatmitctftm fKirtkWui*ti 


mjidnci'frm/f. 


m>2 


.i5i»M^fof'o(f. . 


Uttni 


."'2 


1? 


O- OO- 


'V 


6, 


5 , 41 f 


T 


; 


o 30 T 




't ' 


3 38- 


11 


I 


I oo 4- 


J 


7- 


i tl 


T 


X 


I 29 TT 


t 


T 


3 20 ■!■ 


»tf 


■''± 


'4-' 


8.' 


*■'; "^.''H 


:| 


1 pi 


-«3; ■26 1' ■■' 


"4 


ft 


■* 5*4^ 
■J .■ 5I..V 


''! 


'. 'S'»!i ••}!"■ 


9 


1 




■■ j'od-^ -^ 


■^ 


J. 


r 9 ?■ 


i 


4 


• '3 ■!« i- • 


2 


io 


'', "■■'"',■.■, 


•> 


■./a; 


,j,.j8:t:l 


't.'t 


i.:i'.„V>l 


,? 




1 :»r.,,^ y..1u.U 


V^ 


:r^,'J.,J^ = i^-!K:^H,j,i 


t-jj'ioob--"" 



.■.■-.•■..■\i-ir. 'J tir,(R ,•.*, «tM 



Ii6 The Touttg Survgrt>r*s Gvide, 

the Names of fuch Colours at are necef- • 

faryjor the Wapnng of Maj>s, Charts, 

! or rtofs^ with the manner how to 

tender and ufe the fdtne upon Velom^, 

- . Prf^w (IT Parebmera* 

IT .ii not : canT«nient for ■ Siwveypr 
when be htth~ drawtt the dianght of i i 
Maonor, $nd rrdutcd it to bis thtended j 
bignefi, to repair to a Paiotft to finiOi hit * 
worfc» the thing itfelf bring"' rety commeUT * 
fidblfy and eaue to be atrained : And be> 
lides B Painter is not to be fouDd ifi-eve- 
Tj Cwntr J, nor if every fainter fumiSted 4 
with Q>i°uri futin^f for ibdi a purpore, thejr 
far itwmoft part ^n g mor i gr o f i aod-or'' 
dinary Colours. Now for the benefit of I 
fiH-h who defire to ezerrife themfelres in | 
tfiiiVind of prafiicr, I have addedthelc ne> j 
ceffary dirctSiam following. 

Horn to maJu GnmVater. 

Take Gun Arabicl: what qaantity joa 
plea&« of the whireft and cleareft you can 
gel, which hruife into fmall piecei^ and tie 
them up loofcly in a fine linnen Rag, then 
take of the cleareft Water you can get, and 
pat it into 8 clean veflel, as a poringer, (oc 
itich like) then hang youi Qoath ia wluch 
you 



The Toung Surveyor's Guide, 217 
yon put your Gum into this Water, letting it 
haDg rill all the Gum be dinblved^ then when 
TPa ii^our Fingers into this Watefj if you 
'£nd thnllk to ftick together, as if they were 
"glewred, ybnr Watcrii too fliffof the Gum^ 
-which you may remedy by putting thereto 
more fair Water, aod if you find it too weak, 
you nuv add more Gam } with this Water 
moH Coloun are to be tempered. 

How to rnait Mlum-Water. 

Take a Pound of Allum, and beat it to 
Pofrder, then take a Gallon of clean Water, 
and fet it on a Fire, letting it bail till all the 
Allum be melted, then take it off the Fire, 
and when it is cold you may put it into a 
Teflel and keep it for your ufe : With Ibit 
Water, if you wet your Paper before you 
lay on yotir Colours, it will keep them from 
finking into the Pap^r, and wilt alfo add a 
Lufire lod Beauty to die Colours laid diece- 



The Names offuchColowsti «re neceWaryfor th» 
^afiitigofJ^pSy Ptah, orCbarti. 



REDS. 


ftiAxms. 


BLEWS. 


Vimilliai. 


Owubeme. 


Sice, 
iidifo. 


Sad Lai 


Orpimitt, i,e. 


Vaster: 


w- 


jhjnick 


Ulmofe. 
,L^«d 




L 


Braitl}ei 



■^2 1 8 T'/jtf Toung Surveyot'sG^Ue. 
REDS YELLOftS BLEWS GKEiNS. 
Braxik. ' M-iftkot .UltTamerme Bic^, 
Turj7foUe. S4''o». the btJlBIue.Stp Green. 
Indian Caht. Vertdegrea^, 

Cm mm the Verditure^ 

hejl Red. 
Scat la Flpch 

B L ACK S, WHITES. BROWNS. 

Lamp-Bhck, White S^amjb-Brown. 

Printers-Bhck. Le^d in Umber. 

Ivory iShaxmg fijkei . TfoodSoote. 

Hjfti-Hom T bw«t,. SIndesofGiem 

indiJK-Ink. WaUnutt. 

If. B. Colours made from Vigitables 
fades the fooneft. 

Being thus provided of ihefe feveral Co- 
lours here named, which yo.ii may have ia 
divers places in hpnAov, as alfo of 9 Grijod- 
ing-S'one and Multer, which any- Mafoo 
in London win furniOi jou wiih, alfo di- 
vers Pencils of feveral fizes , and Gally-porf, 
Gar-GUiTes, or Horfe-Mufcle-fhells, to put 
your Colours In when they aie ground and 
tempered, you are then ready at any time 
to m^ke ufe of them, and now- will 1 Oiew 
you how aU the^ forementioned Coloois-arc 
Co be groimd and tetp£*^ea» 



Of 



The Toung Surveyor's Guide, 3 1^ 

Of the orderv'g of Oihurs. 

■ Of t'hefe Colours before mentioned, fome 
are to be Groimd fome Ifafitd^ ibme only 
Steeptd or Diffohed, others to be Boyled, a&i 
Tome to be Burtitj and then Ground. 

1. Hw atiy Cohnrh to be Gromd. 

Take what Quantity of any Colour yt* 
pleafe, that ia to be Grotrnd, and lay it up- 
on jour Grhivig-fime, being clean, as alfo 
your ^»/fcr, then with yoai Muller bruiflt 
the Colour, if it be lompiOi, and when it 
is reafmable fmall or fine, put fome fair 
Vat*r to it, and with your MuUer grind the 
Colour and Tf^'ater together till it be very 
fine ; then with a Kuife or piece of (hin 
Latahan-hont, being clean, take it off iiom 
th&Sfone, and put it into a Shell, and when 
it is dry you may take it out of the Shell, 
and keep it for yoor ufe. 

The Ctlwrt to ^eGratoti are, 

rerm'tSm^Lake, Indigo^ MaJHcot^ WUto-teaii 

In Grinding of your Colours put not too 
much Water to them upon the Stone, for 
they ought to be gtound Stiff, like weak 
Pafte, 01 Pap. 

La 3. Bern 



>30 The'Tottng Sun)eyor*s Gmdsi 

2. Haw Colourt- mt to be Wnfisi, 

■Take a goo^Qpantirj of the Colour wfncfa 
you intend to i^*^; and put it into a ^afm^ 
poaring to it a good Q>ian(ity rf /jir Wattr^ 
and ftir the Colour and tbe Watst oftoi toge- 
ther, and then you will fee a great deal of 
filth IVim at the. top of the ^''ater i when the 
£xi]»ur ii fettled to the bottom of the fiifun^ 
pour away that Water gentlj into anoHter 
VtHel or Bafob, and pour oiorciair Wat^ 
to (he Colour, then ftir the Colour and thrt 
ffflh Water together, Md when the Coloox 
» fettled, pour away (hat fecond -Water to 
the foimer, and (b put'a (bird and fonrtfa 
Water, ftirring it often till the Water come 
from the Colour without filth, then is joat 
Colour Walhed : But before '*ftxx take tb* 
Colour out of the Veflel, lay it with yoor 
Hand very thin about the fide »of the VrfTel, 
snd when it ii dry, fome of it will fall to 
the bottom, which put upon a (heet of Papeii, 
whidi will be good Colour s but the Remain- 
der, which flicks to the.fidei oF the'Bafon, 
is befl of all, which with a Feather Arike 
off the fides of the^VeiTel, for it will be 
•finer than any Flour. 

Tie Colpurx to U Wafbti art^ 

'Seffet. -. Sice Orpiment 

Kid-Ltai Verdittr SffmJb^Brvm- 

- There 



Tk* Toung StdTvejor's GiuJci 221 

TiKfe cr other Colours rhus w^ed. yoU 

may refeive in white Paprr trre fromDtjft, 

and make ule of them as you have occa^on. 

3. How CoJotns are to hs Steeped. 

- This is only to pnt the Cahm into fome' 
kind of Liquor^ and there to diiToIve ; ^onl^ 
io cold Liqaora, others xx\)on the Fire . 

The Cohan to be ^:eped hi cold Liquors are. 



TeUov-Berries, 


Sip-G e:v. 
' Litmofe. 


Qam Bilge. 


Safron. . 


Indian Caket. 



% 



The Colours to he Jheped or billed are, 

Frendf-Verd^reafe. Turvfoil 

Brazil JfoodSoot.^ 
Le^vooi. 

Rhtdes of WaS-nut!, 

Theft Colonrs when fteeped at boiled. are 
to be kept clofe in Glajfes, till you hat'e 
gccafion to ufe them. 

4. Hon' Cohan are to helurytid, 

.Some nfe only to pnt a Lump of Colour 

into a Red-hot place of the Fire, and there 

Jet it lye till it be thoroughly burnt ^ lut this 

L 3 is 



if both wafteful and floveoly. Tbe befi v<I)l 
V tbii. 

Tike a Quantity of your Colovr^zud pnC 
it into a dean Crucible, putting thereto fooie 
Pair witer^ then cover ihe Ciacibk with CTa/, 
arid fet it into a hot place of the Fire, let* 
ting :' t there continue till the Oucible be Red- 
hot, then take it out, tnd when tc it cold 
^ou any take out the CoIunt^ aod gond 
If as ii before taugh\ . 

Tbt Colours to he hwtttare^ 

Spmi^'Brovn. frinters-hUck. luory. 
Ifmber. Lamp-bhck. ffartt^ont 

Or anj other grojt and foul ColoMr. 

Having ihewed you the way how to QrW, 
Wjp, Steeps Boilj and Ban your dlourt^ 1 
will Ihew you now 

y. How to timper^our Cohurti, 

Tirfi, Such Colours as are gromti witV 
Fair-water, take a fmall (Quantity thereof, 
and put it into a MifiUpell, putting there- 
to fome Gum mater^ and the Cvlovr in a fhort 
timewill be molified ; then with your Finger 
(being very clsan) bruife (he Cohvr againfl 
the Shei, tiil you find no jbtott undifTolved^ 
then with a clean ^mcil ftroak down the 
Cdoni towards the bottom of the SbtJl, and 



Ths Thung Surveyor*! Guide, 225 ■ 
it is fit fta afe ; but if it be too thick, add 
more Gum-water to ir. . 

Stich Colntgrs as tnV^afied^ yoH m'jft 
t«(Apei in a SheS tiHItli Gva water^ in llje fame 
niBRnft as yof did tbofe tb«t were Gtoundi 
• Such Colotira is are' Steeped, the Liquor 
osly o[ thbm is to be uTed, witham any 
Addition. 

Of the fivsral Simple Cohtm^ how toor^erthm, 
, without any mixtures, 

I. Of R€ DS, 

Carmine, beirig tempered with wtafe Gum- 
water makes the beft of Reds. 

yermilHvn ,htiH^Gioand and temperea with 
GUpi-Watrr,tiiakes i detpRei otSctriHC^omi 

Lahy Ground aod Tempered with Gum- 
water, makei a deep Pink or Bloom Colour. 

Red t^iJ, Wafiedy is a braW Orient, Co- 
lour, between a Red and an Orarge Colour., 
. Se^r, Wathed, and tempered with Gum- 
wster, differs not much in Colour from 
LakBy bat it will foon fade and grow H^ter, 
W being tempered with Brtoatwjter it will ' 
he more deep. 

Br*iJl, The ShJvifigr or Crtn^rigi ihere- 
i»f being bbiled in Viatgar and fmaM Beer (or 
fail-water) in an Earthen Vefiel, with fome 
powditai JSnm pnt therein to heighten the 
Cofoii?, Slakes an exceUeHt Fini- or ^ight Vidht 
CtieWir When you flrain the Ihiquot from 
1^4 the 



3^4 The Toung Surveyor's Guide* 
the dregs of the Brazil^ add tbcceto fome 
Gum-Arabirk to bind it. 

Tun^ail It is made of Lmm Rttgt ifed* 
which being put into a iSiiiKn- or the ])ke> 
with Coait Vinegar, and ftt upon a Chaiiag' 
diftl of Coals, the Rsigi fqueczed into th* 
TWPfar, with fome Gam to bind it, makes 
a good Colour to fliadow all TeUowt with. 

ht^ati Okei. . Ufe them as yoa do Tant- 
foil^ and they make a good Rei-trmfpareitt 
Colour : loto the Ligaor put fome Gum to 
bind it. 

ScarUtPhch, (which ii bought at the 
Cloatb- Workers,) boiled gentlj in Fair-water 
for about $ Hours, putting a fpoooful of 
Soag-Lett to bring out the Colour { makes 
an excellent Traufparaa - Red , or Scarht 
Colour. 

2. 0/ TELLOirs. 

Gtanhoi^e^ Steeped in Fair water onlf, 
tnakes the moft excellent, and moft tranf- 
pa^ent TeBov Cohur : It is of that Nature, 
that it will admit of no mixture. 

Telloa-Berrhs, Steeped in Fair-vater and 
a little pnwder of ASwn added tbertto 
(or fteeped in Allnm -water) makes a very 
good and Tra^ffparent Tellow. 

Oipimstit^ Wafhed and tempered with 

Gum-water, makes an Orieut or GofdrColoMr, 

tbore 






7i« Toung Survej/or's Guide, 523 
there are feveral degrees of it, fome more 
Red, and others more JeBov. 

Mafiictt^ Ground and tempered with 
Gum-Hrater, makes a good, but no Trarf- 
parent Tellowi: 

SafroHy Steeped in Fair-water all night, 
malces an exciellent Traofparent Gold Cc- 
low. 

3. Of BL UB S. 

UUramerine^ B^ing tempered with a weak 
Gum-water makes the befl Blue. 

Bicty WaOied and tempered with Gum- 
water, is an eicellent Blue, but not tran- 
iparent, and there are feveral foits of it, 
tome lighter fome fadd^. 

itd^Oj Ground and tempered with Gum- 
water, makes a deep ££uf, and it fit to 
fliadow all other Bluet. 

VerdUer, Wafhed and tempered with Gum- 
water, is a good Blue^ but not tranfparent/ 

XAtmofe^ Cat it in fmall llicea, and fteep id 
in a weak Water, made of Gum-Bl»ck, for 
the fpace of a day or more, and you will 
have a trmfparevt Blue. 

Logwood, Boiled in all refpe^ m Brazil^ 
makes an excellent VioUt or Purgk-Cokv, 



4. 



aatf" Tie Totm^ Sttrvejior*i Gukk't 
4^ Of GREENS. 

Bite, Waftied snd tmtppred with Gtam* 
water, makei a good, but no (ranfparent 
Orttn. 

Sap'Orem^ Stcfp'd in Fiir-wtiter, and t lit- 
tle I'owder of Allutn added ihertto^ makea 
a good (rr^BM to Ihadow of damaf^ withat. 

Veriitvre^ WaOied and tempered with 
Gum-water^ makes a Green, noftraofpatent^ ■ 

Haifa pound of Frcncb^^rHgreafe, boHed 
with a Qpart of Fair-wdt«r', putting irt 
in Ounce of Jriol to Wing OBt the Colour, 
makei an excelleAi Tranfparcnt Orem U.- 
fliniog to BIwt. 

N. B. This Colour muft fee boiled very 
gently for aboQt five Honn, then take it 
off the Fire and let it fettle all Kight, 
and the next Mornine pwix off the cleat 
part. 

y. OfBLJCKS. 

hiJi/K'hik^ Grotmd and tempered wird 
a weak Gum-water, it the beft Black fot 
OiiidDwing deeppi' Bbih. 

Lamp-btaiky Prifiters-hljck, Tbory^ Harll- 
Hom Shavings, b?ing Barnt, Ground, and 
Tempered with Gum-water, are all good 
Blacks.. 

6.. 



The Tmng Surveyors Gmde. a a ;r 

e. Of WHITES. 

WTjite-t^eai^ Gronnd and tempered with 
Gum-water, ii the befl V^hiie. 

7. O/RROJTNS. " 

Spam^-Brown^ Burnf, ground and tem- 
pered with Guoi-warer, nuk<;i a Reddifi- 
S^owtt or Liver-Cehur.. 

Umber ^ Burnt, ground, and tempered 
wkh Gum-water, makes a g^nd B^a- 
Co/oar, and ia good to fiadom upuii 
Go!d^ 

M^ooi-S*ot^ or Raist of Tf^all-mtt, K-^iled 
in Fair-water, and flrained, and fomeGum- 
Arabick put into the Liquor, to bind it, either 
of them makes a moll excellent Colour 
£» tp e:^refa High-ways, Laavt, £?'&. 

Of Mixture of Colours. 

fj\' the fore-mentioned Colo'jri that we- 
have hitherto treated of, are fuch as arc 
iimply of themfelves, without any mizf 
tare, of which infinite may be compounded; 
nay, altnoft what you wit). But for- our 
purpofe the moft iranfparent Colours are 
the Principal, fox this our purpofe of Co- 
louring of Plots. Of which Brazil and 
Z/fsvood Water. Carmine, Indian-Cakes. Tum^ 
foil. 



a 2 8 The Toung Surw^er*} Guide, 

foil^ Ultramnjne , Gvmbooge ^ TeUew-berriet^- 
SjffrcH^ Litmofey S'p-Green , Frmch'Verdigreaft^ 
Vtiod-Soot and Wabml-bvfii, are the prin- 
cipal, and of tbefe feversl others may be . 
compounded. 

■ For G REE N. 

Veriigreafe-water , and TeSom-berry-watery , 
makes an excellent tranfparent Grem^ either 
fadder, or lighter, according to tht Quan- 
tity that you take of either. 

For BLUB. 

Utmofc-Vater ^ 'fo which add TelIow4>erry' 
pater^ and you have a fad Grem. 

For OS AN.GE Cohtir.. 

BraxiUgater and TsBoV'btny-wattr, 

%■ In^nite Colours, I Tay, may^be made 
oF theft, which may better be found out by 
pradice d)8n by many words : And there- 
fore Domi- will fhow you what Colours 
do fhadow one another. 

Cimcemittg Shaiowirg. 

All light Cdlouri are fhadowed with 

Colours of ibeir fame Nature but more 

fad. 



■ 



The Tmng Swvejmr's Guide, jjf 
fad , for which take thefe BricF Di- 
redions. 



Virmmn, -1 


tLthfitSimijh-inim 


Vtiiitir mi 

Bk,. 
Gmibxt' ml 




W«». 


. 


VmbtryiAltai-Uai 
or VaiMim. 


Teiou-heniei. 




JUi-LeaJ, 


Is 


Lah,tir Spmifi^om^ 


Mafihote^ 


Sha- 


E,iO,pmM, 


Sfmajt^an. 


SurM U«ber i:b 




ed 


Brnil-vxteT. 


Vmba; 


with 


UnU,n S„,t, 


RofntniSra- 




^anifi-brown ^ mixei 


Jai, Re. 




with Brttzil^waler.. 


Veriipiaft, 




hUfo md n/fcu-fci- 
ri water mixei, 

'Vmkr 


fVoolSmt mi 




rVaUuts, . 




^ 



VMceming the laying on of jow G)- 
* hurt* 



For the Ia]nng oa 61 yoac Colours, 70a 
muft provide jour felf of Pencili tA feveral 
Hzes, bigger and lefl«r, and if jrou will be 
curious, you oi^bt to have a gr^at and a 
fmall to each refpei^ve Colour, if net you 
mtift always have by you a difli of fair- 
water, in which yon muA .fwtll or cteanfe 
your Fenrily wiping it with with a Cleaa, 
IJaen 



13 9 The Toimg Surv^or^s Ouide. 
Linen Cbath, before ^ou put it into ano* 
ther Colour. 

For yonr P*ncilf, you may chnfe,' in 
your buying, tbofe that are good id this 
manner ; See that they be fulleft mit to 
the Quill, dertwiding or leffening into a 
fmall room am} ibarp point, which yoa 
may produce by putting of the Hati mro 
vour Mouth, and drawing it through yoar 
'^pa once or twice, then may yon fee what 
it is, and if yoo find any eitravagant 
Hairs, /inge them off by a Candle's Flame. 

- Being thes provided with Colours and 
Pencils, if you would lay any CoIoot a- 
fiout the fidges of any part or piece of 
Ground in a Plot \ as fuppofe you would 
inclofe a Field in a Plor with fellow j 
with your Pencil take of Gumbooge or 
Tellowr-berrie*, a very fmall Qosnti^yi ^d 
on the infide of the clack-L°ad-line, draw 
the Colour along oT an equal breadth ( ai 
mar at jou.can) iiom. the L'ne, broader or 
narrower, according U your ^^V is in 
bigncfs (wt daidfhig yoar rieli *aSover vttb 
Jomr Cnlowr^ as I bavi feen fame, otherwife 
good tbitgij by this plaftering way ( at I 
may call it) moH nororioufly abufed. Then 
having gone round your Field in this 
manner with your Colour, wet yonr Pen- 
cil in your Month, or have a fmall Qtun- 
tity 



'The Toung Surveyor* s'Guide» 250 
•tily of Water by you to dip it in, and 
IHike along the infide of the Coloured Line, 
bringing it more down roumrda the Center of 
the Field ; and this will fweeten your Co- 
' lour, and ~m3l:e it fhow as if it loft itlelf by 
degrees, to the very Colour of your. Paper 
or Parchment.: And this coqrfe is to be 
taken not only for Tellowt but for all other 
ColcuTi. Then laflly with a Pm (if you 

! cannot handle a fmall Pencil handleinely- 
asd evenly) tak--' (btae of that Colour which 
> fhadoweth that Colour you coloured your 
I Field with, and go over your Black-Lead 
. Line only,fo fhall your Field fee fimfli' 
i <d. 

ArtiJ' in this msnnep nity yott do a Hnn^ 
\ dred Fields in one Plot, of divers Colours: 
' , only obleive this, that as near as you can, 
you colour not two Fields adjoyning one to 
i riw ptber- both of tHe*fsme Colour^ but of 
different: and therefore it will be conveni- 
ent to underftand what Coibura do fet one 
another ofT befl, and as new as you can to lay 
I Clofea. adjoyning one to another, of two fuclj 
^Colouri, that one Shadow may ferve both. 



J? I N I S 






BOOKS Printed for, alid Sold by 
James Knapton at the Crottm in St 
Paul's Chufch-yard. 



IAcobi Rohinlri Ayfin. Laiine venic^ re ceflfDtr^ 
8c ubcricribus pm AnnoianoDibat ex iHaftHfTi' 
mi Ijiaci tkmtni PhiloTophia nuxtnum partem - 
haufHt, amplificarit 6c omivit S. Ciartr. AccedmiE 
edim IB h]c tenU Editionc, dow iliqoot Ta^lx ni 
iacifc; & ABiKxaiionet mohufti funt aoft«, 8vt 
Price 8 1. 

Opr. WiSiam Dtm^kr's Voyiget round die Worid 
jo 3 Vol. 

TheHitloricalGeografhyofthetXd iftdNewTcfti* 
iiKOr, la d Vol. B w. 

The YaaBf Gendeniio't Coofe of MadKfiuHdn, 
t.'^. Arithmetick, Qeomeiry, Tcigoaomeayi Mecha- 
Dicki, Opticki, Aftronomy, ChroDology aod Diailia^ 
in 9 Vol. pr. 1 8 *. 

Harmei^a Grttnmatkalii. 

Mr Wini'tt't AtwhtneacTK, the ijth Edirioa. 

The Artifictil CIock-Makct, by Wm. DrHkm. M. A. 
Rcftor of Vminfltr in fiJT'*) »ud F. R. S. the 3d 
Cdicioti, wirn targe Additioiit,pr. i.s. dd. 

Vfaftt'i Voyaget eo che Ifthmnt of Ameritg, the ad 
Edition. 

Btfman** Defcriptlon of GunVA 

Djf/gn 00 FtuitioDS> ' 

Dtiiiharty\ Gcaenl Ganger IM. adKdiiiDi. 

A Diftionary of all RelieioDf* 

FunoeS't Voyaees raand the World. 

The Rich Man ; Duty to fontribuie liberally to che 
Building, Rebuilding, Repairing and Adataiag of 
Churche*. 









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965 ■ 08 
96?S7« 



SI8601F 
I 9S*5r7 
96(98^ 
96' 454 
9tf79 ' 
9*858? 
6668 irtf 
9'93 3 
9*9789 
9-0'-!4 
92071^9 
97ti8 
671*47 
973110 
972173 
973211 



9613*2 

962705 
9'3W» 

9641 i» 
96468 
9«iS* 
96' 614 



966S6 
9670;- 
.''■ 50 
96796- 
!o84^ 
;6epo3 
pit? 69 
69835 
97 ,0 
I 97076 ■ 
9712:9 

?7l6y3 

97315? 
97X619 
P7Jo8a 







TsoO 






.N 

94° 





'I 

97JI74 


-2 


973«6 


4 


9rin8 


(JJHo 


>7)9IJ 


?4> 


923 » 90 


«73«i« 


91,182 


97)728 


97S774 


94] 


9,4®** 


9)4 97 


?;4'« 


974189 


97ms 


94) 


P74SIX 


9WHl8 


97460) 


974<iSo 


974 9^ 


94 1 


P74971 
975 ig* 


P7joi8 
»7Srt8 


971064 


97J'to 
975S70 


97515* 


975S24 


,754'< 


■ 94tf 


S7J89' 


97J9J7 


-'i485 


9:6029 


9X075 


9fT 


P7'3So 


*7<i9« 


976442 


976)88 


»7<S5»! 


948 


976«afi 


9,«54 


»;6«9J 


976946 


9,6»1 




9777^4 


977112 
9777^9 


>7T?!8 


9774-.1 

977161 


97744» 


977815 


9779JS 


" S^' 


97«i8r 


97821S 


978*72 


978)17 


978 1<5! 


tf5i 


978637 


97848 J 


978728 


>7«774 


978819 


?5j 


979093 


s;9ts8 


97?' 8 1 


9;9X2o 


S79275 


95t 


98000) 


»»SS4 
9^0049 


9800:4 


979685 


979740 


9E0140 


9801 8< 


fi6 


«8o4S! 


980S03 


980(89 


980594 


980640 


'5>5T 


j)8o9ii 


980917 


«8ro03 


981048 


9810,) 


$18 


,I,6< 


98ml 


98,456 


981501 


981547 


9(9 


98217 1 


911864 
982)16 


981909 

9«2!<2 


981954 


98M00 


98'45' 


^> 


5817J5 


9««7fl9 


,8«8li 


98.859 


911904 




?'i"H 


9;3iio 


9*5265 


9|)l.o 


989,54 


SSJMS 


98)671 


y837i6 


9!j7«2 


9«3'07 




9840:7 
J14i'7 


9841 >« 

tS4S72 


98)167 
984617 


984x13 
984662 


584i!7 

»'4T07 


966 


984977 


98501a 


985067 


985111 


985157 


^6? 


989436 


S8S471 


9855.6 


985(6, 


98;6r6 


96 i 


585875 


9*5920 


P«59«! 


oim.o 


98605s 


©Jo 


S 6jS4 

5Laa.77a 


fUltf 


98641 ) 

9868ti 


9B64J8 


986503 


9»ilr6 


986906 


9J-t 


ffljiij 


9I7264 


917)09 


989800 


'='!'! 


p7f 


S»J«6< 


98771. 


»8j7!6 
938 02 


98,846 


97* 


p88l,s 


9S8i(, 


988247 


988295 


fT* 


988 J«9 


9)8604 1988648 198869) '9'»'7JO] 






(sO 



J 


t 


_2_ 


8 


_9_ 





tUi!9 


9»4°S 


97J45I 


973497 


973513 


4* 


973820 


973866 


913913 


971959 


974005 


4-5 


974381 


97na7 


974371 


9744ao 


9744 >« 


■1^ 


97474« 


974788 


9748(4 


974880 


9M9« 


<« 


9yii<a 


975348 


97ja94 


975J40 


9753*' 


4* 


S75<61 


975707 


9757 SJ 


975799 


97584J 


^iS 


57(S.si 


97*1(57 


975JII 


976258 


97*304 


4^' 


97SJ79 


97S<.5 


97«»fi 


97S717 


97«7«» 


4< 


S»77<'37 


97708^ 


9-77129 


977'75 


97714= 


4« 


9771« 
9779Sa 


977H" 
917958 


9775*6 
97»0« 


977631 


977678 


4«S 

4^ 


9780I9 


978135 


97840SI 


»7845, 


978505 


978546 


978S9> 


4< 


»7«I«1 


97891 , 


97895* 


979001 


97904, 


4*5 


9793*1 


979iM 
979eil 
s8o27« 


9794 '3 


979417 


97?5ot 


4« 


8801J, 
9J„<8) 


979867 
98:K3 


979913 


979618 


4* 
4) 


98OJ67 


980412 


'^V,K 


980776 


980S11 


980867 


4; 


981159 


9811*9 


98.275 


sSijio 


4;. 


9|.!9» 


9«.4}7 


98.68* 


58.7!lt 


9' 1773 


M 


98104! 


98159* 


»"n9 


982,81 


982226 


45 


«8j,«7 


9«2S43 


)82|S8 


9'S26„ 


952678 


45 


981949 


9»»994 


(83040 


983085 


983130 


41 


9Sa8!« 


983441S 


98>49, 


9S3536 


» 3!Sf 


41 


18589, 


,8jt4j 


98)987 


Zr. 


^J" 


9843!» 


394147 


93139. 


9S4437 


^ 


9«47!> 


984797 


9 484= 


•!<8i7 


984 3! 


4! 


9'520i 


9*5247 


9ai»9i 


985327 




4' 


9«!<Si 


,85«95 


985741 


9'5 S> 


4' 


98S100 


48(1,4 


98618^ 


986334 


p8 37? 


.5= 


9»'!4! 


9'«.fti 


2866^7 


986682 


986707 


_45 


,16, ,i 


98;04o 


9870'-S 


987130 


96;. 75 


4^ 


!i«74l! 


987488 


9^752) 


987577 


S«7*.a 


4$ 


9»78>o 


987934 


987,79 


9 8014 


9Bao<;<i 


45 


9«8J!« 


98838. 


988425 


968470 


98«,.a 


4^i 


9»l78! 


9S8»i< 


988^71 


98 9 6 


=;.88pdo 


<i: 






f 


■2.~ 




i 







no 






9Ti 





I 


X 


t 


4 


989005 


9BJI049 


98-074 


989138 


98918, 


■^6 


98 4 W- 


9894»4 


9»95»9 


9>9!83 


989«j» 


977 


9« -895 


:«9S,|.-, 


,89,83 


9S00.8 


99107 1 


y7< 


9»J»i9 


■9=5», 


,904.8 


99H7I 


990S111 


;P7.' 
98, 


1>07.J 
991 '.a:- 


9908., 


9.0871 
99'3'S 


9»0!>4« 
99H59 


1909*0 


99121" 


991403 
591845. 


o?t 


Pitet, 


791713 


9917J7 


99i8ji 


9» 


992111 


992 Ji 


99,200 


992244 


992X88 


i>SS 


99>S<4 


992198 


991*42 


992581; 


99*730 


.984 


J9J991 


993039 
9914»i 


993083 
t9!t-4 


993'" 


993172 


99i!68 


993*13 


^8^ 


99J877 


9J!91' 


9939i! 


9,4009 


9940S3 


:»«7 


f94^I7 


9P4J*> 99440J 


974449 


9 4493 


:58il 


994757 


;948oi j 99484r 


594I89 


W4933 


8!f 
P90 


9(i9« 


99 s 240 995284 
99iS-'9\991ji^ 


99S318 
99!7«) 


99!37» 


99s8il 


; 9" 


99io-+ 


9S<II7'99<'«> 


99*103 


99*349 


>9' 


996)12 


996j)j|99<!99 


99**43 


9S,«li8, 


99? 


9 (5949 


991S993 ■ 597037 


997080 


997124 


991 


9^738* 


',97430 997474 


9975 '7 


9973* 


m 


997813 


997 .fi7 9S79IO 
9 «3f» 99»31« 


99^934 


997998 


996 


-991219 


998,90 wy^„ 


997 


9,8«91 


9)1)39 998)81 


99«e,< 9988*9 


,98 


999^ !o 


999'74 999218 


9992*1 97930s 


99f 


999,<S5 


9995091999552 


99 *9*' 999^30 






End(>f 


ttlTa 


ik 












CVt 


J 






5 


6 


7 


8 
989301 


_9_ 

989405 


45^ 


P3S37' 


989316 


.9,612 


9B9717 


SB9761 


989805 


989 so 


.4 


>9oii; 


9SOiii. 


ptfo.os 


99025: 


99029-* 


44 


jg^S*! 


99J'Sos 


990^50 


9?o6,4 


9>o738 , 


44- 


9Pioot 
.91448 


99iS©9 


99io£j 
9915-1* 


991137 


991615 ■ 


44- 


99i5ffo. 


991890 


99 9J4 


991-979 


9j)ioij 


9;2ofi7 


44- 


99^i$i 


991^7 


POinai 


992 16 J 


992505 


44 


'5)2774 


9?i8'9'992gtf3. 


992907 


95295 * 


44 


9j»9iitf 


Py3"o! 993304 


9_nJ4_8 


993 <9i 


-44 


395*57 


?>37oils,9,745 


993789 


5,9383? : 


44. 


99 J 197 


9?4i*» 994-85 


994229 


994373 


;44' 


?94l37 


9J458' 994fi2j 


994*69 


994TIJ 


■;^4' 


59497T 


:99ioii- 99^5, 


995 '08 


995152 


4V 


J)9(8S4 


9PS898- 995943 


99SS47 


995 'P* 


J** 
44 


995985 


995030 


i!9<2p3 


99<Jj37J996j9o 


995*24 


9P54S8 


^4 


99573' 


996774 SpfiBiS 


P?i85fl 


99iSoS 


44 


J97HS3 


9>7=i»i997=S^ 


?97 299 


997043 


44 


9;7«9S 
,9>8o+i 


99808s' 998. »9 


997735 
998372 


997779 


44 
44* 


9/811* 


9p'4-'7 


9?8(ai!998((S4 


^98'!o8 


9y855i| 


44 


«989«^ 


99?9!'i|«9ooo 99Jo^3 


99Po-r 


44 


999418 


99939a 999434- 99. 4791 9?PSi» 


14' 


?99783 


999825 '999670 999^n\9i99ii 


4J 


0/ Lo^^mu - 






"H 


3.. ■ 










TABLE 

or 
' Artifici4 S I N E 5 

I AMD 

I TANGENTS,, 

■ Degree and Minute 

OR' XHE 

QUADRANT. 

Einted to (Ae Size: 
j OE XHE 



so SDOS; 

It 



Simtcii ibc! J^on AflM, at theOoMt 







(5^) 






Degree o \\ 


4 


. Sine 


a O0DO3OO 


Tjpeent 


c. r.«<. 


60 

59 


ooooooc 


C.OOOOOO 

!5.(6372<5 


Infkiiu 


6,4<*?72« 


9.99999 J 


13,538374 


1 


6 7^4756 


■.9999W 


« 7<S47I6 


'J.23?a4, 


58 


it 


6,940847 


9 999999 


5.940847 


i3.»I9'S3 


57 




.7.o6ijae 


9 999999 


7,06 57' S 


il93t(»4 
128*7^04 


Si 


-I 


I7 |6269( 


.9j99£29? 
9.9999-/? 


7j^696 


» 

H 


7 =4' 877 


7.»4i878 


21758111 


1 


7,3<^88«4 


';*i999'^9 


7,30882 s 


12.591175 


1- 


B 


7 ?668i« 


9.999999 


7,3tf68i7 


'M33"83 


5a 




7,4»79« 


v,999999 


7.4 '79 70 


I2i8iojo 


51 


11 


7.4^87^6 

7.505118 


^.999998 


7.46,737 


ia,<>j5a7? 


1° 
49 


9^999999 


7,S£SI20 


I - "" J 


13 


7 5419°'^ 


9.93999.7 


7,441909 


I L 


4* 






9)9*999 .' 


7,577^78 


■ ) 


41 




7,609855 


■ 9><)99996 


7/09857 


) i 


46 


MS 


7M98.( 


9 99P?9* 


7.63^826 


'. I 


44 


7,667844 


9 9>9Pf5 


7,6*7849 






9,999995 


7.69+i79 


1 I 


41 


trt 


7t:»<977 


9^99999^ 


7.71 P003 




4' 


\9 




9999 m 


7,7^2+14 




4» 


la 


7,''«47U 


« 999>« 


7,7fi47tf' 




4? 


7.785$43 


9.999PP2 


7.7«595' 


12,21 04» 


22 


7,So5m£ 


P999?9> 


7.8c6idS 


12193845 


18 






99PM90 


7,»3S4<50 


n.i 7454° 








p 999989 


7,8.. 394 4 


12,156056 


< 


25 


'j,S7ffJ9'5 


9-991.685 


-8tf^«74 


ia,i?83i6 
r2,i)i492 


^4 


9999988 


7B78708 






9 999987 




J 2, 1.04901 


V' 


8R 


?9»o87C 


9 5999*^ 


7,pioBp4 


ia,QS9io(! 


r. 




7,9X51 IS 


9999.8s 


7,925134 




;i 


i? 


? (l„o84a 


**.9tf^. 


7.9*08.8. 


12C59I4.2 


1« 


C» /i»f 


Sine 


a-r^«. 


T«ng«c 




Digrec 85 . 


^ 






C?7> 



IXf rec o [ 


M 

L' 

3.1 

17 

39 

4o 
♦I 
*> 
43 
44 
45 
4« 

s 

4? 
SO 

Jl 

34 

SP 

6o 


Sine 


D, 99998 2 
99^9981 
9,9> 9980 
9 99991^ 
9.999J78 


Tangent. 


CtTMg. 

IZ0^9M2 
11 044900' 

iao3Hii 

•tp'i-ni 
13,00478/ 

"99 J '9' 
1 1.97*95'* 
11,568051 
If 95<<473 
11,94518', 
"■»34'94 
IV 23469 
11,91^003 
11,902783 
ir 89275 7 

11,873490 
I. ,864.49 
II 8J1004 
11,846048 
,(.8j7S73 
II 928673 

n8-,9«4 
1.803844 
IJ.79SB74 
ii,7^8ffl47 
ti,-8oai., 
ii,T?a»o4 
11,7^5379 
H,7iSo79 
Tangcnr. 


i? 
'9- 
l8i 
*7 
US' 
»f 

34 

23 

30 
19 
18 

17 
16 

i_S 

'M 
ij 

II 
10 

1 

7 
6 

A 

1 


M 


7950343 
7,P55^8a 
7.P68870 
7,982233 
7.99SI93 
8£0^8j 

0,OZOO2I 

a.oj.jjrp 
■'.04ii,., 
8, 54781 
3, 0^^7,7.5 

8 07-fs=o 
8,08696 s 
8,097113 
8,10 167 
8,1169X5 


T,94°»^* 
7,?S5«=° 
7 9«8989 

7,9322j? 
7 9S5115 
7,0078X0 
S,OJ0044 
8.031945 
8,043517 
8,o';4Boy 
8,otfi8c6 

8..8*997 
8,097*17 
8,io7»°3 
B,M6-,tf3: 
fl.iltfSlo 
8.13S8S1 
8. '4. 996 
P.'iS'Sa 
9;,tfa737 
8i(7rp8 
8l?97»3 
8,i88oj6 
-.196155 
8,204126 

8,2419 3 
8,219641 
».a2T 9? 
8,23462, 
8,241911 


9 99991 i 
9.99F973 
9,99997= 
9.99997^ 
9,999 sTb 

9 9«99i?^ 
9.9099S4 
9?999 3- 
9-?99?iSi 
9 999^^9 
9.^9P9f8 
PS99:SS 
9-?P99S4 
9 9999r1 
99999%o 
9 99994* 
9>59^94* 
9999944 
9 59J94* 
9P99940 
9 99«9J* 
9999916 
9-9999)4 
Sioc 


l,ia«47i 
8i3S«i' 
8.449':3 
8.IJJ9D; 
8;.tfi 81 


8,i7i;8o 
^,179715 
8187985 
8, 19,6 102 
8ao4o7£ 
8;aii893 
8,ii9{ai 
8,227114 
8,234 J J7 
8.14" 8(5 


CaTa^. 


D<gl««9 












rss J 




DC 


,„.. 




Sine 1 Ctfm. 
8,14185*, P^59934 


Tangent 
8,241921 


CtToH- 


ii.7J?o79 *" 


I 


S,ii4p3j3 999)H'- 


8,J4Pio2 


",7SOJ98 '9 




8,15(5094 


S-i-??*^? 


9,2S«i(S5 


",743835 58 


] 


11,26304; 


95199957 


8.25,„j 


ll,73*88S S7 


4 


8.2518?. 


9 99P9a5 


8,2S9Pi(S 


rr, 7 30044 56 




8.27«I4 


•MP9?sa 


8,i7«Sr 


u. 713309 y 


"i 


C^Vi 


9,9>-9?io 


8,281323 


ii,7itftf77 51 


7 


sl'Sp^yj 


9,9i'99i8 


B28pff5d 


ii,7itfl44 S* 
11,703704 s = 


8 


8.i5<Sao7 


M99J"5 


S,29Sl9t 


9 


8,30254^ 


9,S9;9 13 


o'^ofi^ 


'i,tf973«6 *' 


lO 


8,308794 


9599910 


8,308884 


lI.(?p^It6 If 


■ 1 


8.1I4PS4 


9,999997 


8.315^016 


ir,ea47^ 49 


ct 


8.321017 


PJ'WJOJ 


8,3Jii»2 


H,(i78878 48 


'3 


8.3270'* 


9.999y01 


8327114 


irySjiSSfi 4T 


<4 


r .4 


9 - - )9 


|,3}(oJ5 


llS66sji 4« 


'5 


' il 


p. 7 


8.3j88s< 


".«ii44 45 


16 


8.34450* 


* *'* 


8.344«'° 


ii,tf5S39o 44 


'7 


8,,joiro 


ypppS'pi 


8 350289 


«l.<J<97'i 43 


18 


8.3»S'78} 


9,999888 


8,Jfs89i 


•'.641105 43 


1? 


836-31^ 


9,999885. 


8jtfM3o 


11558570 4' 


ao 


3j«2'i 


p-'-Ja 


8.y<(;8ps 


ii.63fios 4^ 


M 


3 37a»7i 


9 79 


8 3722?! 


ii,<<27-o8 59 


21 


8 37749? 


9999B7S 


8,377^" 


ri,S,2378 5« 


3) 


8.3 Bi 62 


9.999873 


8382889 


'r.tfi7Tir 37 


24 


8,387SSJ 


9 999870 


1 38809.2 


ii.Sirjoe 36 


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9,549" 9 


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9,534920 
9,S1K)84 

9,537400 
9.5a^7S3 
9,(a9i05 
9.528458 
9,1 388 10 
9.sa9"^ 
9.S19JH 

9.530114 

9,53091s 

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9,974*57 
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9.9740 J a 
9.973^87 
9.97394 a 
9.9-7 39' 7 
9,9?38S2 
9.97 3807 
9.9737S1S 
9.9737115 
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9.97 H«9 
9.97 ;44i 

9.973398 
9.913312 
9.973307 
9.973261 
9.97aaii 

9-9731*9 
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10,002374 


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